On nonvanishing of $L$-functions
نویسندگان
چکیده
منابع مشابه
Nonvanishing of L - functions on < ( s ) = 1
In [Ja-Sh], Jacquet and Shalika use the spectral theory of Eisenstein series to establish a new result concerning the nonvanishing of L-functions on <(s) = 1. Specifically they show that the standard L-function L(s, π) of an automorphic cusp form π on GLm is nonzero for <(s) = 1. We analyze this method, make it effective and also compare it with the more standard methods. This note is based on ...
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Let k be a number field with ring of adeles A, let B be a quaternion algebra defined over k, and letG = B×. Let π be an infinite dimensional irreducible cuspidal automorphic representation of G(A). Then the vanishing or nonvanishing of L(1/2, π) has been conjectured or shown to be equivalent to conditions of considerable interest in number theory or automorphic representation theory. For exampl...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1980
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1980-14769-2