non-vanishing. — 2 articles found.

A Weighted Average of $L$-functions of Modular Forms

C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (2) 2021, pp. 63-77
Vol.43 (2) 2021
M. Manickam; V. Kumar Murty, FRSC; E. M. Sandeep Details
(Received: 2021-03-09 , Revised: 2021-04-14 )
(Received: 2021-03-09 , Revised: 2021-04-14 )

M. Manickam , Indian Institute of Science Education and Research Bhopal, Madhya Pradesh 462066 INDIA; e-mail:,

V. Kumar Murty, FRSC,Department of Mathematics, University of Toronto, Ontario, Canada, M5S 2E4; e-mail:

E. M. Sandeep, Kerala School of Mathematics, Kunnamangalam, Kozhikode-673571, Kerala INDIA; e-mail:,


We consider a kernel function introduced by Kohnen and prove an asymptotic formula for a weighted sum of \(L\)-functions of modular forms.

On considère une fonction noyau introduite par Kohnen et démontre une formule asymptotique pour une somme pondérée de fonctions L de forms modulaires.

Keywords: Hecke eigenforms, Modular L-function, cusp forms, full modular group, integral weight, lower bound, non-vanishing.

AMS Subject Classification: Modular forms; one variable, Automorphic forms; one variable, Dirichlet series and functional equations in connection with modular forms 11F11, 11F12, 11F66

PDF(click to download): A Weighted Average of L-functions of Modular Forms

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:


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

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