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Journal De Theorie Des Nombres De Bordeaux最新文献

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Numbers which are only orders of abelian or nilpotent groups 仅仅是阿贝尔群或幂零群的阶数
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1251
Matthew Just
{"title":"Numbers which are only orders of abelian or nilpotent groups","authors":"Matthew Just","doi":"10.5802/jtnb.1251","DOIUrl":"https://doi.org/10.5802/jtnb.1251","url":null,"abstract":"Refining a result of Erdős and Mays, we give asymptotic series expansions for the functions A(x)-C(x), the count of n≤x for which every group of order n is abelian (but not all cyclic), and N(x)-A(x), the count of n≤x for which every group of order n is nilpotent (but not all abelian).","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalization of a density theorem of Khinchin and diophantine approximation Khinchin密度定理与丢番图近似的推广
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1255
József Beck, William W. L. Chen
{"title":"Generalization of a density theorem of Khinchin and diophantine approximation","authors":"József Beck, William W. L. Chen","doi":"10.5802/jtnb.1255","DOIUrl":"https://doi.org/10.5802/jtnb.1255","url":null,"abstract":"The continuous version of a famous result of Khinchin says that a half-infinite torus line in the unit square [0,1] 2 exhibits superdensity, a best form of time-quantitative density, if and only if the slope of the geodesic is a badly approximable number. We extend this result of Khinchin to the case when the unit torus [0,1] 2 is replaced by a finite polysquare translation surface, or square tiled surface. In particular, we show that it is possible to study this very number-theoretic problem by restricting to traditional tools in number theory, using only continued fractions and the famous 3-distance theorem in diophantine approximation combined with an iterative process.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Rational points on symmetric squares of constant algebraic curves over function fields 函数场上常代数曲线对称平方上的有理点
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1252
Jennifer Berg, José Felipe Voloch
{"title":"Rational points on symmetric squares of constant algebraic curves over function fields","authors":"Jennifer Berg, José Felipe Voloch","doi":"10.5802/jtnb.1252","DOIUrl":"https://doi.org/10.5802/jtnb.1252","url":null,"abstract":"We consider smooth projective curves C/𝔽 over a finite field and their symmetric squares C (2) . For a global function field K/𝔽, we study the K-rational points of C (2) . We describe the adelic points of C (2) surviving Frobenius descent and how the K-rational points fit there. Our methods also lead to an explicit bound on the number of K-rational points of C (2) satisfying an additional condition. Some of our results apply to arbitrary constant subvarieties of abelian varieties, however we produce examples which show that not all of our stronger conclusions extend.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sur le biais d’une loi de probabilité relative aux entiers friables 关于易碎整数的概率定律的偏差
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1253
Gérald Tenenbaum
{"title":"Sur le biais d’une loi de probabilité relative aux entiers friables","authors":"Gérald Tenenbaum","doi":"10.5802/jtnb.1253","DOIUrl":"https://doi.org/10.5802/jtnb.1253","url":null,"abstract":"The standard probability law on the set S(x,y) of y-friable integers not exceeding x assigns to each friable integer n a weight proportional to 1/n α , where α=α(x,y) is the saddle-point of the inverse Laplace integral for Ψ(x,y):=|S(x,y)|. This law presents a structural bias inasmuch it weights integers >x. We propose a quantitative measure of this bias and exhibit a related Gaussian distribution.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136295957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Generalized Pell’s equations and Weber’s class number problem 广义佩尔方程与韦伯类数问题
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1249
Hyuga Yoshizaki
{"title":"Generalized Pell’s equations and Weber’s class number problem","authors":"Hyuga Yoshizaki","doi":"10.5802/jtnb.1249","DOIUrl":"https://doi.org/10.5802/jtnb.1249","url":null,"abstract":"We study a generalization of Pell’s equation, whose coefficients are certain algebraic integers. Let X 0 =0 and X n =2+X n-1 for each n∈ℤ ≥1 . We study the ℤ[X n-1 ]-solutions of the equation x 2 -X n 2 y 2 =1. By imitating the solution to the classical Pell’s equation, we introduce new continued fraction expansions for X n over ℤ[X n-1 ] and obtain an explicit solution of the generalized Pell’s equation. In addition, we show that our explicit solution generates all the solutions if and only if the answer to Weber’s class number problem is affirmative. We also obtain a congruence relation for the ratios of the class numbers of the ℤ 2 -extension over the rationals and show the convergence of the class numbers in ℤ 2 .","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136296166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
New p-adic hypergeometric functions and syntomic regulators 新的p进超几何函数和符号调节器
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1250
Masanori Asakura
{"title":"New p-adic hypergeometric functions and syntomic regulators","authors":"Masanori Asakura","doi":"10.5802/jtnb.1250","DOIUrl":"https://doi.org/10.5802/jtnb.1250","url":null,"abstract":"We introduce a new type of p-adic hypergeometric functions, which we call the p-adic hypergeometric functions of logarithmic type. The first main result is to prove the congruence relations that are similar to Dwork’s. The second main result is that the special values of our new functions appear in the syntomic regulators for hypergeometric curves, Fermat curves and some elliptic curves. According to the p-adic Beilinson conjecture by Perrin-Riou, they are expected to be related with the special values of p-adic L-functions. We provide one example for this.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Homothéties explicites des représentations ℓ-adiques Homothéties露骨的描写ℓ-adiques
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1257
Aurélien Galateau, César Martínez
{"title":"Homothéties explicites des représentations ℓ-adiques","authors":"Aurélien Galateau, César Martínez","doi":"10.5802/jtnb.1257","DOIUrl":"https://doi.org/10.5802/jtnb.1257","url":null,"abstract":"This article presents and specifies the main known results on the size of the subgroup of homotheties of ℓ-adic representations associated with the torsion of an abelian variety. Such estimates notably make it possible to give explicit uniform bounds in the framework of the Manin–Mumford problem.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136296035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Potential diagonalisability of pseudo-Barsotti–Tate representations 伪barsotti - tate表象的潜在对角性
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1248
Robin Bartlett
{"title":"Potential diagonalisability of pseudo-Barsotti–Tate representations","authors":"Robin Bartlett","doi":"10.5802/jtnb.1248","DOIUrl":"https://doi.org/10.5802/jtnb.1248","url":null,"abstract":"Previous work of Kisin and Gee proves potential diagonalisability of two dimensional Barsotti–Tate representations of the Galois group of a finite extension K/ℚ p . In this paper we build upon their work by relaxing the Barsotti–Tate condition to one we call pseudo-Barsotti–Tate (which means that for certain embeddings κ:K→ℚ ¯ p we allow the κ-Hodge–Tate weights to be contained in [0,p] rather than [0,1]).","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
ℚ-curves and the Lebesgue–Nagell equation π曲线和Lebesgue-Nagell方程
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1254
Michael A. Bennett, Philippe Michaud-Jacobs, Samir Siksek
{"title":"ℚ-curves and the Lebesgue–Nagell equation","authors":"Michael A. Bennett, Philippe Michaud-Jacobs, Samir Siksek","doi":"10.5802/jtnb.1254","DOIUrl":"https://doi.org/10.5802/jtnb.1254","url":null,"abstract":"for integers x,q,k,y and n, with k≥0 and n≥3. We extend work of the first and third-named authors by finding all solutions in the cases q=41 and q=97. We do this by constructing a Frey–Hellegouarch ℚ-curve defined over the real quadratic field K=ℚ(q), and using the modular method with multi-Frey techniques.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136295784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Computing Euclidean Belyi maps 计算欧几里得Belyi地图
4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI: 10.5802/jtnb.1256
Matthew Radosevich, John Voight
{"title":"Computing Euclidean Belyi maps","authors":"Matthew Radosevich, John Voight","doi":"10.5802/jtnb.1256","DOIUrl":"https://doi.org/10.5802/jtnb.1256","url":null,"abstract":"We exhibit an explicit algorithm to compute three-point branched covers of the complex projective line when the uniformizing triangle group is Euclidean.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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