Nonvanishing of \(GL(2)\) automorphic \(L\)-functions at \(1/2\) (Q1277283)
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scientific article; zbMATH DE number 1248101
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonvanishing of \(GL(2)\) automorphic \(L\)-functions at \(1/2\) |
scientific article; zbMATH DE number 1248101 |
Statements
Nonvanishing of \(GL(2)\) automorphic \(L\)-functions at \(1/2\) (English)
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14 July 1999
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The author relates the nonvanishing at 1/2 of the standard \(L\)-function of an irreducible cuspidal automorphic representation of \(GL(2)\) with trivial central character to the nonvanishing of certain trilinear forms. He also gives applications to modular forms. The main ingredients are some results of Waldspurger, and the method of seesaw dual pairs from the theory of the theta correspondence.
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nonvanishing of the standard \(L\)-function of an irreducible cuspidal automorphic representation
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nonvanishing of trilinear forms
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modular forms
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seesaw dual pairs
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theta correspondence
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