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

C. R. Math. Rep. Acad. Sci. Canada Vol. 28 (2) 2006, pp. 33–38

June 30, 2006

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

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