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Moscow Journal of Combinatorics and Number Theory最新文献

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Algebraic results for the values 𝜗3(mτ) and𝜗3(nτ) of the Jacobi theta-constant 值的代数结果𝜗3（mτ）和𝜗Jacobiθ常数的3（nτ）
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-01-01 DOI: 10.2140/MOSCOW.2019.8.71
C. Elsner, F. Luca, Y. Tachiya
{"title":"Algebraic results for the values 𝜗3(mτ) and\u0000𝜗3(nτ) of the Jacobi theta-constant","authors":"C. Elsner, F. Luca, Y. Tachiya","doi":"10.2140/MOSCOW.2019.8.71","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.71","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/MOSCOW.2019.8.71","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46335756","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: 4
Transcendence of numbers related with Cahen’sconstant 与卡亨常数有关的数的超越
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-01-01 DOI: 10.2140/MOSCOW.2019.8.57
D. Duverney, T. Kurosawa, I. Shiokawa
{"title":"Transcendence of numbers related with Cahen’s\u0000constant","authors":"D. Duverney, T. Kurosawa, I. Shiokawa","doi":"10.2140/MOSCOW.2019.8.57","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.57","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/MOSCOW.2019.8.57","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43633724","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
To the reader 致读者
Moscow Journal of Combinatorics and Number Theory Pub Date : 2019-01-01 DOI: 10.2140/MOSCOW.2019.8.1
N. Moshchevitin, A. Raigorodskii
{"title":"To the reader","authors":"N. Moshchevitin, A. Raigorodskii","doi":"10.2140/MOSCOW.2019.8.1","DOIUrl":"https://doi.org/10.2140/MOSCOW.2019.8.1","url":null,"abstract":"","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/MOSCOW.2019.8.1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41757700","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 products of shifts in arbitrary fields 关于任意域中位移的乘积
Moscow Journal of Combinatorics and Number Theory Pub Date : 2018-12-05 DOI: 10.2140/moscow.2019.8.247
A. Warren
{"title":"On products of shifts in arbitrary fields","authors":"A. Warren","doi":"10.2140/moscow.2019.8.247","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.247","url":null,"abstract":"We adapt the approach of Rudnev, Shakan, and Shkredov to prove that in an arbitrary field $mathbb{F}$, for all $A subset mathbb{F}$ finite with $|A| < p^{1/4}$ if $p:= Char(mathbb{F})$ is positive, we have $$|A(A+1)| gtrsim |A|^{11/9}, qquad |AA| + |(A+1)(A+1)| gtrsim |A|^{11/9}.$$ This improves upon the exponent of $6/5$ given by an incidence theorem of Stevens and de Zeeuw.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.247","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46133895","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: 4
On a theorem of Hildebrand 关于希尔德布兰德的一个定理
Moscow Journal of Combinatorics and Number Theory Pub Date : 2018-10-02 DOI: 10.2140/moscow.2019.8.189
C. Dietzel
{"title":"On a theorem of Hildebrand","authors":"C. Dietzel","doi":"10.2140/moscow.2019.8.189","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.189","url":null,"abstract":"We prove that for each multiplicative subgroup $A$ of finite index in $mathbb{Q}^+$, the set of integers $a$ with $a, a+1 in A$ is an IP-set. This generalizes a theorem of Hildebrand concerning completely multiplicative functions taking values in the $k$-th roots of unity.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.189","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43841360","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
Value-distribution of quartic HeckeL-functions 四次heckel函数的值分布
Moscow Journal of Combinatorics and Number Theory Pub Date : 2018-09-26 DOI: 10.2140/moscow.2021.10.167
Peng Gao, Liangyi Zhao
{"title":"Value-distribution of quartic Hecke\u0000L-functions","authors":"Peng Gao, Liangyi Zhao","doi":"10.2140/moscow.2021.10.167","DOIUrl":"https://doi.org/10.2140/moscow.2021.10.167","url":null,"abstract":"Set $K=mathbb{Q}(i)$ and suppose that $cin mathbb{Z}[i]$ is a square-free algebraic integer with $cequiv 1 imod{langle16rangle}$. Let $L(s,chi_{c})$ denote the Hecke $L$-function associated with the quartic residue character modulo $c$. For $sigma>1/2$, we prove an asymptotic distribution function $F_{sigma}$ for the values of the logarithm of begin{equation*} L_c(s)= L(s,chi_c)L(s,overline{chi}_{c}), end{equation*} as $c$ varies. Moreover, the characteristic function of $F_{sigma}$ is expressed explicitly as a product over the prime ideals of $mathbb{Z}[i]$.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44702639","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
Generalized Beatty sequences and complementary triples 广义Beatty序列与互补三元组
Moscow Journal of Combinatorics and Number Theory Pub Date : 2018-09-10 DOI: 10.2140/moscow.2019.8.325
J. Allouche, F. Michel Dekking
{"title":"Generalized Beatty sequences and complementary triples","authors":"J. Allouche, F. Michel Dekking","doi":"10.2140/moscow.2019.8.325","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.325","url":null,"abstract":"A generalized Beatty sequence is a sequence $V$ defined by $V(n)=plfloor{nalpha}rfloor+qn +r$, for $n=1,2,dots$, where $alpha$ is a real number, and $p,q,r$ are integers. These occur in several problems, as for instance in homomorphic embeddings of Sturmian languages in the integers. Our results are for the case that $alpha$ is the golden mean, but we show how some results generalise to arbitrary quadratic irrationals. We mainly consider the following question: For which sixtuples of integers $p,q,r,s,t,u$ are the two sequences $V=(plfloor{nalpha}rfloor+qn +r)$ and $W=(slfloor{nalpha}rfloor+tn +u)$ complementary sequences? \u0000We also study complementary triples, i.e., three sequences $V_i=(p_ilfloor{nalpha}rfloor+q_in+r_i), :i=1,2,3$, with the property that the sets they determine are disjoint with union the positive integers.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.325","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68081206","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: 12
A family of four-variable expanders with quadratic growth 具有二次增长的四变量扩展器族
Moscow Journal of Combinatorics and Number Theory Pub Date : 2018-05-11 DOI: 10.2140/moscow.2019.8.143
Mehdi Makhul
{"title":"A family of four-variable expanders with quadratic growth","authors":"Mehdi Makhul","doi":"10.2140/moscow.2019.8.143","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.143","url":null,"abstract":"We prove that if $g(x,y)$ is a polynomial of constant degree $d$ that $y_2-y_1$ does not divide $g(x_1,y_1)-g(x_2,y_2)$, then for any finite set $A subset mathbb{R}$ [ |X| gg_d |A|^2, quad text{where} X:=left{frac{g(a_1,b_1)-g(a_2,b_2)}{b_2-b_1} :, a_1,a_2,b_1,b_2 in A right}. ] We will see this bound is also tight for some polynomial $g(x,y)$.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.143","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46459789","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
Integer complexity: the integer defect 整数复杂性：整数缺陷
Moscow Journal of Combinatorics and Number Theory Pub Date : 2018-04-20 DOI: 10.2140/moscow.2019.8.193
Harry Altman
{"title":"Integer complexity: the integer defect","authors":"Harry Altman","doi":"10.2140/moscow.2019.8.193","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.193","url":null,"abstract":"Define $|n|$ to be the complexity of $n$, the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. John Selfridge showed that $|n|ge 3log_3 n$ for all $n$, leading this author and Zelinsky to define the defect of $n$, $delta(n)$, to be the difference $|n|-3log_3 n$. Meanwhile, in the study of addition chains, it is common to consider $s(n)$, the number of small steps of $n$, defined as $ell(n)-lfloorlog_2 nrfloor$, an integer quantity. So here we analogously define $D(n)$, the integer defect of $n$, an integer version of $delta(n)$ analogous to $s(n)$. Note that $D(n)$ is not the same as $lceil delta(n) rceil$. \u0000We show that $D(n)$ has additional meaning in terms of the defect well-ordering considered in [3], in that $D(n)$ indicates which powers of $omega$ the quantity $delta(n)$ lies between when one restricts to $n$ with $|n|$ lying in a specified congruence class modulo $3$. We also determine all numbers $n$ with $D(n)le 1$, and use this to generalize a result of Rawsthorne [18].","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.193","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42213072","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: 5
On the quotient set of the distance set 在距离集的商集上
Moscow Journal of Combinatorics and Number Theory Pub Date : 2018-02-22 DOI: 10.2140/moscow.2019.8.103
A. Iosevich, D. Koh, Hans Parshall
{"title":"On the quotient set of the distance set","authors":"A. Iosevich, D. Koh, Hans Parshall","doi":"10.2140/moscow.2019.8.103","DOIUrl":"https://doi.org/10.2140/moscow.2019.8.103","url":null,"abstract":"Let ${Bbb F}_q$ be a finite field of order $q.$ We prove that if $dge 2$ is even and $E subset {Bbb F}_q^d$ with $|E| ge 9q^{frac{d}{2}}$ then $$ {Bbb F}_q=frac{Delta(E)}{Delta(E)}=left{ frac{a}{b}: a in Delta(E), b in Delta(E) backslash {0} right},$$ where $$ Delta(E)={||x-y||: x,y in E}, ||x||=x_1^2+x_2^2+cdots+x_d^2.$$ If the dimension $d$ is odd and $Esubset mathbb F_q^d$ with $|E|ge 6q^{frac{d}{2}},$ then $$ {0}cupmathbb F_q^+ subset frac{Delta(E)}{Delta(E)},$$ where $mathbb F_q^+$ denotes the set of nonzero quadratic residues in $mathbb F_q.$ Both results are, in general, best possible, including the conclusion about the nonzero quadratic residues in odd dimensions.","PeriodicalId":36590,"journal":{"name":"Moscow Journal of Combinatorics and Number Theory","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2140/moscow.2019.8.103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44160285","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: 11
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