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Abstract intersection theory for zeta-functions: geometric aspects zeta函数的抽象交理论：几何方面
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-06-01 DOI: 10.7169/FACM/1916
Grzegorz Banaszak, Y. Uetake
{"title":"Abstract intersection theory for zeta-functions: geometric aspects","authors":"Grzegorz Banaszak, Y. Uetake","doi":"10.7169/FACM/1916","DOIUrl":"https://doi.org/10.7169/FACM/1916","url":null,"abstract":"","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48980004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The construction of the Hilbert genus fields of real cyclic quartic fields 实数循环四次域的Hilbert属域的构造
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-05-24 DOI: 10.7169/facm/2014
M. M. Chems-Eddin, Moulay Ahmed Hajjami, M. Taous
{"title":"The construction of the Hilbert genus fields of real cyclic quartic fields","authors":"M. M. Chems-Eddin, Moulay Ahmed Hajjami, M. Taous","doi":"10.7169/facm/2014","DOIUrl":"https://doi.org/10.7169/facm/2014","url":null,"abstract":"Let k be a number field and let H(k) denote the Hilbert class field of k, that is the maximal abelian unramified extension of k. It is known by class field theory that the Galois group of the extension H(k)/k, i.e., G := Gal(H(k)/k), is isomorphic to Cl(k), the class group of k (cf. [13, p. 228]). The Hilbert genus field of k, denoted by E(k), is the invariant field of G. Thus, by Galois theory, we have: Cl(k)/Cl(k) ≃ G/G ≃ Gal(E(k)/k),","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44343428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On sign changes of primitive Fourier coefficients of Siegel cusp forms 关于Siegel尖点形式的原始傅立叶系数的符号变化
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-03-25 DOI: 10.7169/facm/2101
K. D. Shankhadhar, P. Tiwari
{"title":"On sign changes of primitive Fourier coefficients of Siegel cusp forms","authors":"K. D. Shankhadhar, P. Tiwari","doi":"10.7169/facm/2101","DOIUrl":"https://doi.org/10.7169/facm/2101","url":null,"abstract":"In this article, we establish quantitative results for sign changes in certain subsequences of primitive Fourier coefficients of a non-zero Siegel cusp form of arbitrary degree over congruence subgroups. As a corollary of our result for degree two Siegel cusp forms, we get sign changes of its diagonal Fourier coefficients. In the course of our proofs, we prove the non-vanishing of certain type of Fourier-Jacobi coefficients of a Siegel cusp form and all theta components of certain Jacobi cusp forms of arbitrary degree over congruence subgroups, which are also of independent interest.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43693186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Euler sums of generalized hyperharmonic numbers 广义超调和数的Euler和
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-03-19 DOI: 10.7169/facm/1953
Rusen Li
{"title":"Euler sums of generalized hyperharmonic numbers","authors":"Rusen Li","doi":"10.7169/facm/1953","DOIUrl":"https://doi.org/10.7169/facm/1953","url":null,"abstract":"are the generalized hyperharmonic numbers (see [4, 10]). Furthermore, H (p,1) n = H (p) n = ∑n j=1 1/n p are the generalized harmonic numbers and H (1,r) n = h (r) n are the classical hyperharmonic numbers. In particularH (1,1) n = Hn are the classical harmonic numbers. Many researchers have been studying Euler sums of harmonic and hyperharmonic numbers (see [4, 6, 7, 9] and references therein), since they play","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47163246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Small prime solutions of a Diophantine equation with one prime and five cubes of primes 具有一个素数和五个素数立方的丢芬图方程的小素数解
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-03-01 DOI: 10.7169/FACM/1874
Weiping Li
{"title":"Small prime solutions of a Diophantine equation with one prime and five cubes of primes","authors":"Weiping Li","doi":"10.7169/FACM/1874","DOIUrl":"https://doi.org/10.7169/FACM/1874","url":null,"abstract":"Let $a_1,cdots,a_6$ be non-zero integers satisfying $(a_i,a_j)=1, 1leq i lt j leq 6$ and $b$ be any integer. For the Diophantine equation $a_1p_1+a_2p_2^3+cdots+a_6p_6^3=b$ we prove that (i) if all $a_1,cdots,a_6$ are positive and $bgg max {|a_j|}^{34+varepsilon}$, then the equation is soluble in primes $p_j$, and (ii) if $a_1,cdots,a_6$ are not all of the same sign, then the equation has prime solutions satisfying $max { p_1,p_2^3,cdots,p_6^3 }ll |b|+max {|a_j|}^{33+varepsilon}$, where the implied constants depend only on $varepsilon$.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45672076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the distribution of the $lcm$ of $k$-tuples and related problems 关于$k$-元组的$lcm$的分布及相关问题
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-02-10 DOI: 10.7169/facm/2008
Sungjin Kim
{"title":"On the distribution of the $lcm$ of $k$-tuples and related problems","authors":"Sungjin Kim","doi":"10.7169/facm/2008","DOIUrl":"https://doi.org/10.7169/facm/2008","url":null,"abstract":"We study the distribution of the least common multiple of positive integers in N ∩ [1 , x ] and related problems. We refine some results of Hilberdink and T´oth (2016). We also give a partial result toward a conjecture of Hilberdink, Luca, and T´oth (2020).","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48879660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Elliptic curves with a point of order $13$ defined over cyclic cubic fields 循环三次域上定义的阶点为$13$的椭圆曲线
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-14 DOI: 10.7169/facm/1945
Peter Bruin, M. Derickx, M. Stoll
{"title":"Elliptic curves with a point of order $13$ defined over cyclic cubic fields","authors":"Peter Bruin, M. Derickx, M. Stoll","doi":"10.7169/facm/1945","DOIUrl":"https://doi.org/10.7169/facm/1945","url":null,"abstract":"We show that there is essentially a unique elliptic curve E defined over a cubic Galois extension K of Q with a K-rational point of order 13 and such that E is not defined over Q.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44333860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effective uniform approximation by $ L$-functionsin the Selberg class Selberg类中$L$-函数的有效一致逼近
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-12 DOI: 10.7169/facm/2026
K. Endo
{"title":"Effective uniform approximation by $ L$-functionsin the Selberg class","authors":"K. Endo","doi":"10.7169/facm/2026","DOIUrl":"https://doi.org/10.7169/facm/2026","url":null,"abstract":"Recently, Garunkštis, Laurinc̆ikas, Matsumoto, J. & R. Steuding showed an effective universality-type theorem for the Riemann zeta-function by using an effective multidimensional denseness result of Voronin. We will generalize Voronin’s effective result and their theorem to the elements of the Selberg class satisfying some conditions.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49569847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pairs of equiperimeter and equiareal triangles whose sides are perfect squares 等长三角形边为完全正方形的等长三角形对
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1985
A. Choudhry, A. S. Zargar
{"title":"Pairs of equiperimeter and equiareal triangles whose sides are perfect squares","authors":"A. Choudhry, A. S. Zargar","doi":"10.7169/facm/1985","DOIUrl":"https://doi.org/10.7169/facm/1985","url":null,"abstract":"In this paper we consider the problem of finding pairs of triangles whose sides are perfect squares of integers, and which have a common perimeter and common area. We find two such pairs of triangles, and prove that there exist infinitely many pairs of triangles with the specified properties. Mathematics Subject Classification 2020: 11D41","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44679867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions 向量值超函数的渐近傅立叶变换和拉普拉斯变换
IF 0.5
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI Pub Date : 2021-01-01 DOI: 10.7169/facm/1955
K. Kruse
{"title":"Asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions","authors":"K. Kruse","doi":"10.7169/facm/1955","DOIUrl":"https://doi.org/10.7169/facm/1955","url":null,"abstract":"We study Fourier and Laplace transforms for Fourier hyperfunctions with values in a complex locally convex Hausdorff space. Since any hyperfunction with values in a wide class of locally convex Hausdorff spaces can be extended to a Fourier hyperfunction, this gives simple notions of asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions, which improves the existing models of Komatsu, Bäumer, Lumer and Neubrander and Langenbruch.","PeriodicalId":44655,"journal":{"name":"FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45746409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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