Non-vanishing of periods of automorphic functions (Q2716428)
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scientific article; zbMATH DE number 1598942
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Non-vanishing of periods of automorphic functions |
scientific article; zbMATH DE number 1598942 |
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Non-vanishing of periods of automorphic functions (English)
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20 May 2001
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period of automorphic function
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critical \(L\)-value
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analytic vector
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automorphic representation
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The author discusses nonvanishing of certain periods of automorphic functions on GL(2). He gives a lower bound on the average size of such a period which is essentially sharp (Theorem~2). The proof of the Theorem 2 is based on the prinicple of analytic continuation of vectors in a representation of GL(2) [\textit{J. Bernstein} and \textit{A. Reznikov}, Ann. Math. (2) 150, 329-350 (1999; Zbl 0934.11023)]. As an application he obtains the nonvanishing of a class of triple product \(L\)-functions at \(s={1\over 2}\) (Corollaries 2 and 3).
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