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Journal De Theorie Des Nombres De Bordeaux最新文献

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Brauer–Manin obstruction for zero-cycles on certain varieties 某些品种上零环的Brauer-Manin阻塞
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-11-11 DOI: 10.5802/jtnb.1241
Evis Ieronymou
{"title":"Brauer–Manin obstruction for zero-cycles on certain varieties","authors":"Evis Ieronymou","doi":"10.5802/jtnb.1241","DOIUrl":"https://doi.org/10.5802/jtnb.1241","url":null,"abstract":"We investigate the question of whether the existence of a family of local zero-cycles of degree $d$ orthogonal to the Brauer group implies the non-emptiness of the Brauer-Manin set for certain varieties. We provide various examples of Brauer-Manin obstruction to the existence of zero-cycles of appropriate degrees.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44764447","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
Classical forms of weight one in ordinary families 在普通家庭中，传统的重量形式是一种
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-11-08 DOI: 10.5802/jtnb.1242
Eric Stubley
{"title":"Classical forms of weight one in ordinary families","authors":"Eric Stubley","doi":"10.5802/jtnb.1242","DOIUrl":"https://doi.org/10.5802/jtnb.1242","url":null,"abstract":"We develop a new strategy for studying low weight specializations of $p$-adic families of ordinary modular forms. In the elliptic case, we give a new proof of a result of Ghate--Vatsal which states that a Hida family contains infinitely many classical eigenforms of weight one if and only if it has complex multiplication. Our strategy is designed to explicitly avoid use of the related facts that the Galois representation attached to a classical weight one eigenform has finite image, and that classical weight one eigenforms satisfy the Ramanujan conjecture. We indicate how this strategy might be used to prove similar statement in the case of partial weight one Hilbert modular forms, given a suitable development of Hida theory in that setting.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48022238","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
Extremal Sidon Sets are Fourier Uniform, with Applications to Partition Regularity 极值西顿集是傅里叶一致的，并应用于划分正则性
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-10-26 DOI: 10.5802/jtnb.1239
Miquel Ortega, Sean M. Prendiville
{"title":"Extremal Sidon Sets are Fourier Uniform, with Applications to Partition Regularity","authors":"Miquel Ortega, Sean M. Prendiville","doi":"10.5802/jtnb.1239","DOIUrl":"https://doi.org/10.5802/jtnb.1239","url":null,"abstract":"Generalising results of ErdH{o}s-Freud and Lindstr\"om, we prove that the largest Sidon subset of a bounded interval of integers is equidistributed in Bohr neighbourhoods. We establish this by showing that extremal Sidon sets are Fourier-pseudorandom, in that they have no large non-trivial Fourier coefficients. As a further application we deduce that, for any partition regular equation in five or more variables, every finite colouring of an extremal Sidon set has a monochromatic solution.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48887107","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
Approximation of values of algebraic elements over the ring of power sums 幂和环上代数元素值的近似
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-10-19 DOI: 10.5802/jtnb.1247
C. Fuchs, Sebastian Heintze
{"title":"Approximation of values of algebraic elements over the ring of power sums","authors":"C. Fuchs, Sebastian Heintze","doi":"10.5802/jtnb.1247","DOIUrl":"https://doi.org/10.5802/jtnb.1247","url":null,"abstract":"Let $ mathbb{Q}mathcal{E}_{mathbb{Z}} $ be the set of power sums whose characteristic roots belong to $ mathbb{Z} $ and whose coefficients belong to $ mathbb{Q} $, i.e. $ G : mathbb{N} rightarrow mathbb{Q} $ satisfies begin{equation*} G(n) = G_n = b_1 c_1^n + cdots + b_h c_h^n end{equation*} with $ c_1,ldots,c_h in mathbb{Z} $ and $ b_1,ldots,b_h in mathbb{Q} $. Furthermore, let $ f in mathbb{Q}[x,y] $ be absolutely irreducible and $ alpha : mathbb{N} rightarrow overline{mathbb{Q}} $ be a solution $ y $ of $ f(G_n,y) = 0 $, i.e. $ f(G_n,alpha(n)) = 0 $ identically in $ n $. Then we will prove under suitable assumptions a lower bound, valid for all but finitely many positive integers $ n $, for the approximation error if $ alpha(n) $ is approximated by rational numbers with bounded denominator. After that we will also consider the case that $ alpha $ is a solution of begin{equation*} f(G_n^{(0)}, ldots, G_n^{(d)},y) = 0, end{equation*} i.e. defined by using more than one power sum and a polynomial $ f $ satisfying some suitable conditions. This extends results of Bugeaud, Corvaja, Luca, Scremin and Zannier.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41246434","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
Linear Relations of Siegel Poincaré Series and Non-vanishing of the Central Values of Spinor L-functions 西格尔庞卡罗级数的线性关系及旋量l函数中心值的不消失性
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-10-12 DOI: 10.5802/jtnb.1226
Zhining Wei
{"title":"Linear Relations of Siegel Poincaré Series and Non-vanishing of the Central Values of Spinor L-functions","authors":"Zhining Wei","doi":"10.5802/jtnb.1226","DOIUrl":"https://doi.org/10.5802/jtnb.1226","url":null,"abstract":"In this paper, we will first investigate the linear relations of a one parameter family of Siegel Poincaré series. Then we give the applications to the non-vanishing of Fourier coefficients of Siegel cusp eigenforms and the central values.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41706869","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
Correction to the paper “Kolyvagin’s result on the vanishing of Ш(E/K)[p ∞ ] and its consequences for anticyclotomic Iwasawa theory” 对论文“Kolyvagin关于Ш(E/K)[p∞]消失的结果及其对抗细胞分裂Iwasawa理论的影响”的更正
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-09-10 DOI: 10.5802/jtnb.1172
Ahmed Matar, J. Nekovář
{"title":"Correction to the paper “Kolyvagin’s result on the vanishing of Ш(E/K)[p ∞ ] and its consequences for anticyclotomic Iwasawa theory”","authors":"Ahmed Matar, J. Nekovář","doi":"10.5802/jtnb.1172","DOIUrl":"https://doi.org/10.5802/jtnb.1172","url":null,"abstract":"","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48835980","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
The distribution of numbers with many ordered factorizations 具有多个有序因子分解的数的分布
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-09-10 DOI: 10.5802/jtnb.1170
Noah Lebowitz-Lockard
{"title":"The distribution of numbers with many ordered factorizations","authors":"Noah Lebowitz-Lockard","doi":"10.5802/jtnb.1170","DOIUrl":"https://doi.org/10.5802/jtnb.1170","url":null,"abstract":"L’accès aux articles de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.centre-mersenne.org/), implique l’accord avec les conditions générales d’utilisation (http://jtnb. centre-mersenne.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46423084","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
A higher-order generalization of Jacobi’s derivative formula and its algebraic geometric analogue 雅可比导数公式的高阶推广及其代数几何类比
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-09-10 DOI: 10.5802/jtnb.1164
David Grant
{"title":"A higher-order generalization of Jacobi’s derivative formula and its algebraic geometric analogue","authors":"David Grant","doi":"10.5802/jtnb.1164","DOIUrl":"https://doi.org/10.5802/jtnb.1164","url":null,"abstract":"We generalize Jacobi’s derivative formula for odd m by writing an m × m determinant of higher order derivatives at 0 of theta functions in 1 variable with characteristic vectors with entries in 1 2mZ as an explicit constant times a power of Dedekind’s η-function. We do so by deriving it from an algebraic geometric version that holds in characteristic not dividing 6m. Introduction In the vast pantheon of theta function identities, a central position is held by Jacobi’s derivative formula. Recall that for τ ∈ h = {x+ iy | y > 0}, and a, b ∈ R, we define the theta function in one variable z ∈ C with characteristic vector [ a b ] by (1) θ [ a b ] (z, τ) = ∑ n∈Z eπi(n+a) τ+2πi(n+a)(z+b). A characteristic vector [ a b ] with a, b ∈ 1 2Z is called a theta characteristic, which is called odd or even depending on whether θ [ a b ] (z, τ) is an odd or even function of z. Modulo 1 there is a unique odd theta characteristic δ := [ 1/2 1/2 ] , and three even ones, 1 := [ 0 0 ] , 2 := [ 1/2 0 ] , 3 := [ 0 1/2 ] . Manuscrit reçu le 6 février 2020, révisé le 2 février 2021, accepté le 18 mai 2021. 2010 Mathematics Subject Classification. 14K25, 14H42. Mots-clefs. Theta functions, elliptic curves.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48757562","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
On the ℓ-adic valuation of certain Jacobi sums 关于某些Jacobi和的r -进值
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-09-10 DOI: 10.5802/jtnb.1171
V. Arul
{"title":"On the ℓ-adic valuation of certain Jacobi sums","authors":"V. Arul","doi":"10.5802/jtnb.1171","DOIUrl":"https://doi.org/10.5802/jtnb.1171","url":null,"abstract":"Jacobi sums are ubiquitous in number theory, and congruences often provide a helpful way to study them. A p-adic congruence for Jacobi sums comes from Stickelberger’s congruence, and various `-adic congruences have been studied in [Eva98], [Mik87], [Iwa75], [Iha86], and [Ueh87]. We establish a new `-adic congruence for certain Jacobi sums.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44322211","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
On the Decomposition of Hecke Polynomials over Parabolic Hecke Algebras 关于抛物型Hecke代数上Hecke多项式的分解
IF 0.4 4区 数学
Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-08-10 DOI: 10.5802/jtnb.1235
Claudius Heyer
{"title":"On the Decomposition of Hecke Polynomials over Parabolic Hecke Algebras","authors":"Claudius Heyer","doi":"10.5802/jtnb.1235","DOIUrl":"https://doi.org/10.5802/jtnb.1235","url":null,"abstract":"We generalize a classical result of Andrianov on the decomposition of Hecke polynomials. Let F be a non-archimedean local fied. For every connected reductive group G, we give a criterion for when a polynomial with coefficients in the spherical parahoric Hecke algebra of G(F) decomposes over a parabolic Hecke algebra associated with a non-obtuse parabolic subgroup of G. We classify the non-obtuse parabolics. This then shows that our decomposition theorem covers all the classical cases due to Andrianov and Gritsenko. We also obtain new cases when the relative root system of G contains factors of types E6 or E7.","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49527766","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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