Mathematika最新文献

{"title":"Extremal values of semi-regular continuants and codings of interval exchange transformations","authors":"Alessandro De Luca,&nbsp;Marcia Edson,&nbsp;Luca Q. Zamboni","doi":"10.1112/mtk.12185","DOIUrl":"10.1112/mtk.12185","url":null,"abstract":"<p>Given a set <math>\u0000 <semantics>\u0000 <mi>A</mi>\u0000 <annotation>$mathbb {A}$</annotation>\u0000 </semantics></math> consisting of positive integers <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>a</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>&lt;</mo>\u0000 <msub>\u0000 <mi>a</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>&lt;</mo>\u0000 <mi>⋯</mi>\u0000 <mo>&lt;</mo>\u0000 <msub>\u0000 <mi>a</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$a_1&lt;a_2&lt;cdots &lt;a_k$</annotation>\u0000 </semantics></math> and a <i>k</i>-term partition <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>P</mi>\u0000 <mo>:</mo>\u0000 <msub>\u0000 <mi>n</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <msub>\u0000 <mi>n</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <mi>⋯</mi>\u0000 <mo>+</mo>\u0000 <msub>\u0000 <mi>n</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <mo>=</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$P: n_1+n_2 + cdots + n_k=n$</annotation>\u0000 </semantics></math>, find the extremal denominators of the regular and semi-regular continued fraction <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mn>0</mn>\u0000 <mo>;</mo>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>,</mo>\u0000 <mtext>…</mtext>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$[0;x_1,x_2,ldots ,x_n]$</annotation>\u0000 </semantics></math> with partial quotients <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>x</mi>\u0000 <mi>i</mi>\u0000 </msub>\u0000 <mo>∈</mo>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <annotation>$x_iin mathbb {A}$</annotation>\u0000 </semantics></math> and where each <math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>a</mi>\u0000 <mi>i</mi>\u0000 </msub>\u0000 <annotation>$","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48323863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The distribution of geodesics on the cube surface","authors":"Yuxuan Yang","doi":"10.1112/mtk.12188","DOIUrl":"10.1112/mtk.12188","url":null,"abstract":"<p>We establish a Kronecker–Weyl type result, on time-quantitative equidistribution for a natural non-integrable system, geodesic flow on the cube surface. Our tool is the shortline-ancestor method developed in Beck, Donders, and Yang [Acta Math. Hungar. <b>161</b> (2020), 66–184] and Beck, Donders, and Yang [Acta Math. Hungar. <i>162</i> (2020), 220–324], modified in an appropriate way to embrace all slopes. The method is further enhanced by the symmetry of the cube through the use of the irreducible representations of the symmetric group <i>S</i>₄ which makes the determination of the irregularity exponent substantially simpler.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49016445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Average shadowing and gluing property","authors":"Michael Blank","doi":"10.1112/mtk.12187","DOIUrl":"10.1112/mtk.12187","url":null,"abstract":"<p>The purpose of this work is threefold: (i) extend shadowing theory for discontinuous and non-invertible systems, (ii) consider more general classes of perturbations (for example, small only on average), (iii) establish a general theory based on the property that the shadowing holds for the case of a single perturbation. The “gluing” construction used in the analysis of the last property turns out to be the key point of this theory.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46323401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the number variance of zeta zeros and a conjecture of Berry","authors":"Meghann Moriah Lugar,&nbsp;Micah B. Milinovich,&nbsp;Emily Quesada-Herrera","doi":"10.1112/mtk.12184","DOIUrl":"10.1112/mtk.12184","url":null,"abstract":"<p>Assuming the Riemann hypothesis, we prove estimates for the variance of the real and imaginary part of the logarithm of the Riemann zeta function in short intervals. We give three different formulations of these results. Assuming a conjecture of Chan for how often gaps between zeros can be close to a fixed non-zero value, we prove a conjecture of Berry (1988) for the number variance of zeta zeros in the non-universal regime. In this range, Gaussian unitary ensemble statistics do not describe the distribution of the zeros. We also calculate lower order terms in the second moment of the logarithm of the modulus of the Riemann zeta function on the critical line. Assuming Montgomery's pair correlation conjecture, this establishes a special case of a conjecture of Keating and Snaith (2000).</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12184","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47571627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On strong chains of sets and functions","authors":"Tanmay C. Inamdar","doi":"10.1112/mtk.12183","DOIUrl":"10.1112/mtk.12183","url":null,"abstract":"<p>Shelah has shown that there are no chains of length ω₃ increasing modulo finite in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow></mrow>\u0000 <msub>\u0000 <mi>ω</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </msup>\u0000 <msub>\u0000 <mi>ω</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>${}^{omega _2}omega _2$</annotation>\u0000 </semantics></math>. We improve this result to sets. That is, we show that there are no chains of length ω₃ in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <msub>\u0000 <mi>ω</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mi>ℵ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 </msup>\u0000 <annotation>$[omega _2]^{aleph _2}$</annotation>\u0000 </semantics></math> increasing modulo finite. This contrasts with results of Koszmider who has shown that there are, consistently, chains of length ω₂ increasing modulo finite in <math>\u0000 <semantics>\u0000 <msup>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <msub>\u0000 <mi>ω</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mi>ℵ</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </msup>\u0000 <annotation>$[omega _1]^{aleph _1}$</annotation>\u0000 </semantics></math> as well as in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow></mrow>\u0000 <msub>\u0000 <mi>ω</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </msup>\u0000 <msub>\u0000 <mi>ω</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>${}^{omega _1}omega _1$</annotation>\u0000 </semantics></math>. More generally, we study the depth of function spaces <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow></mrow>\u0000 <mi>κ</mi>\u0000 </msup>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 <annotation>${}^kappa mu$</annotation>\u0000 ","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12183","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48463431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discorrelation of multiplicative functions with nilsequences and its application on coefficients of automorphic L-functions","authors":"Xiaoguang He,&nbsp;Mengdi Wang","doi":"10.1112/mtk.12182","DOIUrl":"10.1112/mtk.12182","url":null,"abstract":"<p>We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that the above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two applications of this result. One is that the twisting of coefficients of automorphic <i>L</i>-function on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>m</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>⩾</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$GL_m (m geqslant 2)$</annotation>\u0000 </semantics></math> and polynomial nilsequences has logarithmic decay; the other is that the mean value of the Möbius function, coefficients of automorphic <i>L</i>-function, and polynomial nilsequences also has logarithmic decay.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12182","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48068428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exponentially larger affine and projective caps","authors":"Christian Elsholtz,&nbsp;Gabriel F. Lipnik","doi":"10.1112/mtk.12173","DOIUrl":"10.1112/mtk.12173","url":null,"abstract":"<p>In spite of a recent breakthrough on upper bounds of the size of cap sets (by Croot, Lev and Pach and by Ellenberg and Gijswijt), the classical cap set constructions had not been affected. In this work, we introduce a very different method of construction for caps in all affine spaces with odd prime modulus <i>p</i>. Moreover, we show that for all primes <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>≡</mo>\u0000 <mn>5</mn>\u0000 <mspace></mspace>\u0000 <mi>mod</mi>\u0000 <mspace></mspace>\u0000 <mn>6</mn>\u0000 </mrow>\u0000 <annotation>$p equiv 5 bmod 6$</annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>⩽</mo>\u0000 <mn>41</mn>\u0000 </mrow>\u0000 <annotation>$p leqslant 41$</annotation>\u0000 </semantics></math>, the new construction leads to an exponentially larger growth of the affine and projective caps in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>AG</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>${rm AG}(n,p)$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>PG</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>p</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>${rm PG}(n,p)$</annotation>\u0000 </semantics></math>. For example, when <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mn>23</mn>\u0000 </mrow>\u0000 <annotation>$p=23$</annotation>\u0000 </semantics></math>, the existence of caps with growth <math>\u0000 <semantics>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>8.0875</mn>\u0000 <mtext>…</mtext>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$(8.0875ldots )^n$</annotation>\u0000 </semantics></math> follows from a three-dimensional example of Bose, and the only improvement had been to <math>\u0000 <semantics>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>8.0901</mn>\u0000 <mtext>…</mtext>\u0000 <mo>)</mo>\u0000 </m","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12173","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9390986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correlations of multiplicative functions in function fields","authors":"Oleksiy Klurman,&nbsp;Alexander P. Mangerel,&nbsp;Joni Teräväinen","doi":"10.1112/mtk.12181","DOIUrl":"10.1112/mtk.12181","url":null,"abstract":"<p>We develop an approach to study character sums, weighted by a multiplicative function <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>:</mo>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mi>t</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <mo>→</mo>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$fcolon mathbb {F}_q[t]rightarrow S^1$</annotation>\u0000 </semantics></math>, of the form\u0000\u0000 </p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12181","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48206343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric generalizations of the square sieve, with an application to cyclic covers","authors":"Alina Bucur,&nbsp;Alina Carmen Cojocaru,&nbsp;Matilde N. Lalín,&nbsp;Lillian B. Pierce","doi":"10.1112/mtk.12180","DOIUrl":"10.1112/mtk.12180","url":null,"abstract":"<p>We formulate a general problem: Given projective schemes <math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$mathbb {Y}$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$mathbb {X}$</annotation>\u0000 </semantics></math> over a global field <i>K</i> and a <i>K</i>-morphism η from <math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$mathbb {Y}$</annotation>\u0000 </semantics></math> to <math>\u0000 <semantics>\u0000 <mi>X</mi>\u0000 <annotation>$mathbb {X}$</annotation>\u0000 </semantics></math> of finite degree, how many points in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>(</mo>\u0000 <mi>K</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {X}(K)$</annotation>\u0000 </semantics></math> of height at most <i>B</i> have a pre-image under η in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Y</mi>\u0000 <mo>(</mo>\u0000 <mi>K</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {Y}(K)$</annotation>\u0000 </semantics></math>? This problem is inspired by a well-known conjecture of Serre on quantitative upper bounds for the number of points of bounded height on an irreducible projective variety defined over a number field. We give a nontrivial answer to the general problem when <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>T</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$K=mathbb {F}_q(T)$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mi>Y</mi>\u0000 <annotation>$mathbb {Y}$</annotation>\u0000 </semantics></math> is a prime degree cyclic cover of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>X</mi>\u0000 <mo>=</mo>\u0000 <msubsup>\u0000 <mi>P</mi>\u0000 <mi>K</mi>\u0000 <mi>n</mi>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$mathbb {X}=mathbb {P}_{K}^n$</annotation>\u0000 </semantics></math>. Our tool is a new geometric sieve, which generalizes the polynomial sieve to a geometric setting over global function fields.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48518388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discrete isoperimetric problems in spaces of constant curvature","authors":"Bushra Basit,&nbsp;Zsolt Lángi","doi":"10.1112/mtk.12175","DOIUrl":"10.1112/mtk.12175","url":null,"abstract":"<p>The aim of this paper is to prove isoperimetric inequalities for simplices and polytopes with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$d+2$</annotation>\u0000 </semantics></math> vertices in Euclidean, spherical and hyperbolic <i>d</i>-space. In particular, we find the minimal volume <i>d</i>-dimensional hyperbolic simplices and spherical tetrahedra of a given inradius. Furthermore, we investigate the properties of maximal volume spherical and hyperbolic polytopes with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$d+2$</annotation>\u0000 </semantics></math> vertices with a given circumradius, and the hyperbolic polytopes with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$d+2$</annotation>\u0000 </semantics></math> vertices with a given inradius and having a minimal volume or minimal total edge length. Finally, for any <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>⩽</mo>\u0000 <mi>k</mi>\u0000 <mo>⩽</mo>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 <annotation>$1 leqslant k leqslant d$</annotation>\u0000 </semantics></math>, we investigate the properties of Euclidean simplices and polytopes with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$d+2$</annotation>\u0000 </semantics></math> vertices having a fixed inradius and a minimal volume of its <i>k</i>-skeleton. The main tool of our investigation is Euclidean, spherical and hyperbolic Steiner symmetrization.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.12175","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43250441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}