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

Abstract/Résumé:

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