L-functions — 3 articles found.

On $L^{(r+1)}(\pi,1/2)$

C. R. Math. Rep. Acad. Sci. Canada Vol. 28 (2) 2006, pp. 33–38
Vol.28 (2) 2006
Amir Akbary Details
(Received: 2005-11-15 )
(Received: 2005-11-15 )

Amir Akbary, Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive West, Lethbridge, Alberta T1K 3M4; email: amir.akbary@uleth.ca


Let \(r\) be the order of vanishing of the automorphic \(L\)-function \(L(\pi,s)\) at \(s=1/2\). We study the non-vanishing of the derivative of order \(r+1\) of \(L(\pi,s)\) at \(s=1/2\).

Soit \(r\) l’ordre d’annulation de la fonction \(L\) automorphe \(L(\pi,s)\) à \(s=1/2\). Nous étudions la non-annulation de la dérivée d’ordre \(r+1\) de \(L(\pi,s)\) à \(s=1/2\).

Keywords: L-functions, non-vanishing of high derivatives of L-functions

AMS Subject Classification: Special values of automorphic $L$-series; periods of modular forms; cohomology; modular symbols 11F67

PDF(click to download): On $L^{(r+1)}(pi,1/2)$

A non-vanishing theorem on Dirichlet series

C. R. Math. Rep. Acad. Sci. Canada Vol. 27, (3), 2005 pp. 76–83
Vol.27 (3) 2005
Wentang Kuo Details
(Received: 2005-03-09 )
(Received: 2005-03-09 )

Wentang Kuo, Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1; email: wtkuo@math.uwaterloo.ca


The non-vanishing property of certain Dirichlet series is a fundamental problem in analytic number theory. In this paper, we provide a non-vanishing theorem, which is a generalization of Ogg’s result. We apply our theorem to get applications on distributions of eigenvalues of Hecke eigenforms and recover the non-vanishing theorem for the \(L\)-functions of cuspidal representations.

La propriété non nulle de certaines séries de Dirichlet est un problème fondamental dans la théorie analytique des nombres. Dans cet article, nous fournissons un théorème non-non-vanishing, qui est une généralisation du résultat d’Ogg. Nous appliquons notre théorème pour obtenir des applications sur des distributions des valeurs propres des opérateurs de Hecke et nous récupèrous théorème non nulle pour les \(L\)-fonctions des représentations cuspidales.

Keywords: L-functions, elliptic curves, non-vanishing.

AMS Subject Classification: Modular and automorphic functions 11F03

PDF(click to download): A non-vanishing theorem on Dirichlet series

Summatory functions of elements in Selberg’s class II

C. R. Math. Rep. Acad. Sci. Canada Vol. 25 (2) 2003, pp. 55–62
Vol.25 (2) 2003
W. Kuo Details
(Received: 2003-01-23 )
(Received: 2003-01-23 )

W. Kuo


No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: L-functions, Selberg class

AMS Subject Classification: Other Dirichlet series and zeta functions 11M41

PDF(click to download): Summatory functions of elements in Selberg's class II

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