The Ramanujan Journal最新文献_第7页

Arithmetic properties and asymptotic formulae for $$sigma _otext {mex}(n)$$ and $$sigma _etext {mex}(n)$$ $$sigma _otext {mex}(n)$$ 和 $$sigma _etext {mex}(n)$$ 的算术性质和渐近公式

The Ramanujan Journal Pub Date : 2024-06-24 DOI: 10.1007/s11139-024-00886-7

Rupam Barman, Gurinder Singh

引用次数: 0

On the Lang–Trotter conjecture for a class of non-generic abelian surfaces 关于一类非一般无常曲面的 Lang-Trotter 猜想

The Ramanujan Journal Pub Date : 2024-06-23 DOI: 10.1007/s11139-024-00884-9

Mohammed Amin Amri

引用次数: 0

The density of the graph of elliptic Dedekind sums 椭圆戴德金和图的密度

The Ramanujan Journal Pub Date : 2024-06-22 DOI: 10.1007/s11139-024-00880-z

Stephen Bartell, Abby Halverson, Brenden Schlader, Siena Truex, Tian An Wong

引用次数: 0

Spectral moments of the real Ginibre ensemble 真实吉尼布雷合奏的谱矩

The Ramanujan Journal Pub Date : 2024-06-21 DOI: 10.1007/s11139-024-00879-6

Sung-Soo Byun, Peter J. Forrester

{"title":"Spectral moments of the real Ginibre ensemble","authors":"Sung-Soo Byun, Peter J. Forrester","doi":"10.1007/s11139-024-00879-6","DOIUrl":"https://doi.org/10.1007/s11139-024-00879-6","url":null,"abstract":"The moments of the real eigenvalues of real Ginibre matrices are investigated from the viewpoint of explicit formulas, differential and difference equations, and large N expansions. These topics are inter-related. For example, a third-order differential equation can be derived for the density of the real eigenvalues, and this can be used to deduce a second-order difference equation for the general complex moments (M_{2p}^textrm{r}). The latter are expressed in terms of the ({}_3 F_2) hypergeometric functions, with a simplification to the ({}_2 F_1) hypergeometric function possible for (p=0) and (p=1), allowing for the large N expansion of these moments to be obtained. The large N expansion involves both integer and half-integer powers of 1/N. The three-term recurrence then provides the large N expansion of the full sequence ({ M_{2p}^textrm{r} }_{p=0}^infty ). Fourth- and third-order linear differential equations are obtained for the moment generating function and for the Stieltjes transform of the real density, respectively, and the properties of the large N expansion of these quantities are determined.","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141513240","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

$$mathbb {Z}_2$$ -extension of real quadratic fields with $$mathbb {Z}/2mathbb {Z}$$ as 2-class group at each layer 实二次域的 $$mathbb {Z}_2$$ 扩展，每层的 2 类群为 $$mathbb {Z}/2mathbb {Z}$$

The Ramanujan Journal Pub Date : 2024-06-17 DOI: 10.1007/s11139-024-00869-8

H. Laxmi, Anupam Saikia

引用次数: 0

Dirichlet series and -log 2 狄利克特数列和-log 2

The Ramanujan Journal Pub Date : 2024-06-14 DOI: 10.1007/s11139-024-00856-z

Gaspar Mora

引用次数: 0

On effective irrationality exponents of cubic irrationals 论立方无理数的有效无理指数

The Ramanujan Journal Pub Date : 2024-05-28 DOI: 10.1007/s11139-024-00877-8

Dzmitry Badziahin

引用次数: 0

On the solutions of $$x^2= By^p+Cz^p$$ and $$2x^2= By^p+Cz^p$$ over totally real fields 关于完全实域上 $$x^2= By^p+Cz^p$$ 和 $$2x^2= By^p+Cz^p$$ 的解

The Ramanujan Journal Pub Date : 2024-05-28 DOI: 10.1007/s11139-024-00881-y

Narasimha Kumar, Satyabrat Sahoo

引用次数: 0

The average behaviour of Fourier coefficients of the Hecke–Maass form associated to k-free numbers 与无 k 数相关的 Hecke-Maass 形式的傅立叶系数的平均行为

The Ramanujan Journal Pub Date : 2024-05-27 DOI: 10.1007/s11139-024-00876-9

Guodong Hua

引用次数: 0

On matching and periodicity for $$(N,alpha )$$ -expansions 关于$$(N,alpha )$$ 展开的匹配性和周期性

The Ramanujan Journal Pub Date : 2024-05-27 DOI: 10.1007/s11139-024-00878-7

Cor Kraaikamp, Niels Langeveld

{"title":"On matching and periodicity for $$(N,alpha )$$ -expansions","authors":"Cor Kraaikamp, Niels Langeveld","doi":"10.1007/s11139-024-00878-7","DOIUrl":"https://doi.org/10.1007/s11139-024-00878-7","url":null,"abstract":"Recently a new class of continued fraction algorithms, the ((N,alpha ))-expansions, was introduced in Kraaikamp and Langeveld (J Math Anal Appl 454(1):106–126, 2017) for each (Nin mathbb {N}), (Nge 2) and (alpha in (0,sqrt{N}-1]). Each of these continued fraction algorithms has only finitely many possible digits. These ((N,alpha ))-expansions ‘behave’ very different from many other (classical) continued fraction algorithms; see also Chen and Kraaikamp (Matching of orbits of certain n-expansions with a finite set of digits (2022). To appear in Tohoku Math. J arXiv:2209.08882), de Jonge and Kraaikamp (Integers 23:17, 2023), de Jonge et al. (Monatsh Math 198(1):79–119, 2022), Nakada (Tokyo J Math 4(2):399–426, 1981) for examples and results. In this paper we will show that when all digits in the digit set are co-prime with N, which occurs in specified intervals of the parameter space, something extraordinary happens. Rational numbers and certain quadratic irrationals will not have a periodic expansion. Furthermore, there are no matching intervals in these regions. This contrasts sharply with the regular continued fraction and more classical parameterised continued fraction algorithms, for which often matching is shown to hold for almost every parameter. On the other hand, for (alpha ) small enough, all rationals have an eventually periodic expansion with period 1. This happens for all (alpha ) when (N=2). We also find infinitely many matching intervals for (N=2), as well as rationals that are not contained in any matching interval.","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169637","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