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Publications Mathématiques de Besançon最新文献

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Sur les minima des formes hamiltoniennes binaires définies positives 关于正定二元哈密顿形式的最小值
Publications Mathématiques de Besançon Pub Date : 2021-05-12 DOI: 10.5802/PMB.39
G. Chenevier, F. Paulin
{"title":"Sur les minima des formes hamiltoniennes binaires définies positives","authors":"G. Chenevier, F. Paulin","doi":"10.5802/PMB.39","DOIUrl":"https://doi.org/10.5802/PMB.39","url":null,"abstract":"Etant donne un ordre maximal $O$ d'une algebre de quaternions rationnelle definie $A$ de discriminant $D_A$, nous montrons que le minimum des formes hamiltoniennes binaires sur $O$, definies positives et de discriminant $−1$, est $sqrt{D_A}$. Lorsque la differente de $O$ est principale, nous explicitons une forme atteignant cette valeur, et lorsque $O$ est principal, nous donnons la liste exacte des formes atteignant cette valeur. Nous donnons des criteres et des algorithmes pour determiner quand la differente de $O$ est principale.","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"121 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122933576","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
An introduction to classical and finite multiple zeta values 介绍经典的和有限的多重zeta值
Publications Mathématiques de Besançon Pub Date : 2019-10-15 DOI: 10.5802/pmb.31
M. Kaneko
{"title":"An introduction to classical and finite multiple zeta values","authors":"M. Kaneko","doi":"10.5802/pmb.31","DOIUrl":"https://doi.org/10.5802/pmb.31","url":null,"abstract":"—We review some basic properties of multiple zeta values, in particular the theory of regularization and its connection to an identity between certain integral and series discovered in collaboration with S. Yamamoto. We also introduce the two “finite” versions of multiple zeta values, and a conjectural connection between them, which were discovered jointly with D. Zagier. Résumé. — (Une introduction aux valeurs des fonctions zétas multiples)Nous décrivons certaines propriétés basiques des valeurs de fonctions zétas multiples. Nous explicitons en particulier la théorie des régularisations et son lien avec une identité, obtenue en collaboration avec S. Yamamoto, entre certaines intégrales et séries. Nous présentons également les deux versions finies des valeurs zétas multiples et un lien conjectural entre elles découvert conjointement avec D. Zagier.","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122187034","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: 25
Polygones fondamentaux d’une courbe modulaire 模曲线的基本多边形
Publications Mathématiques de Besançon Pub Date : 2018-09-11 DOI: 10.5802/PMB.40
K. Belabas, D. Bernardi, B. Perrin-Riou
{"title":"Polygones fondamentaux d’une courbe modulaire","authors":"K. Belabas, D. Bernardi, B. Perrin-Riou","doi":"10.5802/PMB.40","DOIUrl":"https://doi.org/10.5802/PMB.40","url":null,"abstract":"A few pages in Siegel describe how, starting with a fundamental polygon for a compact Riemann surface, one can construct a symplectic basis of its homology. This note retells that construction, specializing to the case where the surface is associated to a congruence subgroup $Gamma$ of $SL_2(Z)$. One then obtains by classical procedures a generating system for $Gamma$ with a minimal number of hyperbolic elements and a presentation of the $Z[Gamma]$-module $Z[P^1(Q)]_0$.","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127319655","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
A three-parameter clan of Hurwitz–Belyi maps Hurwitz-Belyi地图的三参数族
Publications Mathématiques de Besançon Pub Date : 2018-06-20 DOI: 10.5802/PMB.22
D. Roberts
{"title":"A three-parameter clan of Hurwitz–Belyi maps","authors":"D. Roberts","doi":"10.5802/PMB.22","DOIUrl":"https://doi.org/10.5802/PMB.22","url":null,"abstract":"— We study a collection of Hurwitz–Belyi maps depending on three integer parameters, finding formulas uniform in the parameters. Résumé. — (Une famille d’applications d’Hurwitz–Belyi à trois paramètres) Nous étudions une certaine collection d’applications d’Hurwitz–Belyi dépendant de trois paramètres avec l’obtention de formules uniformes.","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125451995","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
A partial Bombieri–Vinogradov theorem with explicit constants 具有显式常数的部分Bombieri-Vinogradov定理
Publications Mathématiques de Besançon Pub Date : 2018-06-20 DOI: 10.5802/PMB.24
A. Sedunova
{"title":"A partial Bombieri–Vinogradov theorem with explicit constants","authors":"A. Sedunova","doi":"10.5802/PMB.24","DOIUrl":"https://doi.org/10.5802/PMB.24","url":null,"abstract":"— In this paper we improve the result of [1] with getting (log x) 2 instead of (log x) 2 . In particular we obtain a better version of Vaughan’s inequality by applying the explicit variant of an inequality connected to the Möbius function from [5]. Résumé. — (Aspects explicites d’un théorème de Bombieri–Vinogradov) Dans cet article, nous améliorons un résultat de [1] en remplaçant le (log x) 2 par un (log x) 2 . En particulier, nous obtenons une version améliorée de l’inégalité de Vaughan en appliquant une version explicite d’une inégalité dans [5] liée à la fonction de Möbius.","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"9 2-4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116818798","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
Jacobi sums and Grössencharacters 雅可比和Grössencharacters
Publications Mathématiques de Besançon Pub Date : 2018-06-20 DOI: 10.5802/PMB.25
M. Watkins
{"title":"Jacobi sums and Grössencharacters","authors":"M. Watkins","doi":"10.5802/PMB.25","DOIUrl":"https://doi.org/10.5802/PMB.25","url":null,"abstract":"— In 1952, Weil published a paper describing how to interpret Jacobi sums in terms of Hecke Grössencharacters of cyclotomic fields. We describe an explicit version of this, with reference to our previous work concerning algorithmic implementation of Grössencharacters. We correct various errors involving root numbers in the latter, and also indicate how Jacobi sum methods can be used to understand tame primes of hypergeometric motives. Résumé. — (Sommes de Jacobi et Grössencharacters) En 1952, Weil a publié un article dans lequel il donne une interprétation des sommes de Jacobi en terme de Hecke Grössencharacters de corps cyclotomiques. Nous décrivons une version explicite de cette interprétation en lien avec un travail précédent sur l’implantation algorithmique des Grössencharacters. Nous corrigeons à ce sujet quelques erreurs liées au root numbers. Nous expliquons également comment la méthode des sommes de Jacobi peut être utilisée pour comprendre le comportement de la ramification modérée des motifs hypergéométriques.","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116363702","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
Sur la comparaison entre les minima et les pentes 最小值和坡度的比较
Publications Mathématiques de Besançon Pub Date : 2018-06-20 DOI: 10.5802/PMB.20
Huayi Chen
{"title":"Sur la comparaison entre les minima et les pentes","authors":"Huayi Chen","doi":"10.5802/PMB.20","DOIUrl":"https://doi.org/10.5802/PMB.20","url":null,"abstract":"On etudie la comparaison entre les minima et les pentes successifs d'un fibre vectoriel hermitien sur une courbe arithmetique et demontre un encadrement uniform de leurs differences.","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"650 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132126207","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
A strategy and a new operator to generate covariants in small characteristic 一种生成小特征协变的策略和新算子
Publications Mathématiques de Besançon Pub Date : 2018-06-20 DOI: 10.5802/pmb.23
Florent Ulpat Rovetta
{"title":"A strategy and a new operator to generate covariants in small characteristic","authors":"Florent Ulpat Rovetta","doi":"10.5802/pmb.23","DOIUrl":"https://doi.org/10.5802/pmb.23","url":null,"abstract":"","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124045039","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
Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks 数列加权象限行走的微分超越性及代数准则
Publications Mathématiques de Besançon Pub Date : 2017-09-20 DOI: 10.5802/pmb.29
T. Dreyfus, K. Raschel
{"title":"Differential transcendence & algebraicity criteria for the series counting weighted quadrant walks","authors":"T. Dreyfus, K. Raschel","doi":"10.5802/pmb.29","DOIUrl":"https://doi.org/10.5802/pmb.29","url":null,"abstract":"We consider weighted small step walks in the positive quadrant, and provide algebraicity and differential transcendence results for the underlying generating functions: we prove that depending on the probabilities of allowed steps, certain of the generating series are algebraic over the field of rational functions, while some others do not satisfy any algebraic differential equation with rational functions coefficients. Our techniques involve differential Galois theory for difference equations as well as complex analysis (Weierstrass parameterization of elliptic curves). We also extend to the weighted case many key intermediate results, as a theorem of analytic continuation of the generating functions.","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"2018 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121859040","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: 15
Lifting of Modular Forms 模式的提升
Publications Mathématiques de Besançon Pub Date : 2017-05-23 DOI: 10.5802/pmb.27
Jitendra Bajpai
{"title":"Lifting of Modular Forms","authors":"Jitendra Bajpai","doi":"10.5802/pmb.27","DOIUrl":"https://doi.org/10.5802/pmb.27","url":null,"abstract":"The existence and construction of vector-valued modular forms (vvmf) for any arbitrary Fuchsian group $mathrm{G}$, for any representation $rho:mathrm{G} longrightarrow mathrm{GL}_{d}(mathbb{C})$ of finite image can be established by lifting scalar-valued modular forms of the finite index subgroup $Ker(rho)$ of $mathrm{G}$. In this article vvmf are explicitly constructed for any admissible multiplier (representation) $rho$, see Section 3 for the definition of admissible multiplier. In other words, the following question has been partially answered: For which representations $rho$ of a given $mathrm{G}$, is there a vvmf with at least one nonzero component ?","PeriodicalId":194637,"journal":{"name":"Publications Mathématiques de Besançon","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125377984","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
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