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Annales mathématiques du Québec

, Volume 38, Issue 1, pp 1–6 | Cite as

Rationality of secant zeta values

  • Pierre Charollois
  • Matthew Greenberg
Article

Abstract

We use the theory of generalized \(\eta \)-functions to prove a conjecture of Lalín, Rodrigue and Rogers concerning the algebraic nature of special values of the secant zeta function.

Keywords

Rationality Secant zeta values Functional equations \(\eta \)-Functions 

Résumé

Nous utilisons la théorie des fonctions \(\eta \) généralisées pour prouver une conjecture de Lalín, Rodrigue et Rogers concernant la nature algébrique de valeurs spéciales de la fonction zeta sécante.

Mathematics Subject Classification

11F11 

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Copyright information

© Fondation Carl-Herz and Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institut de mathématiques de JussieuUniversité Paris 6ParisFrance
  2. 2.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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