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A converse theorem for

โœ Scribed by J.B. Conrey; David W. Farmer; B.E. Odgers; N.C. Snaith

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
129 KB
Volume
122
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

We prove that a Dirichlet series with a functional equation and Euler product of a particular form can only arise from a holomorphic cusp form on the Hecke congruence group ฮ“ 0 (13). The proof does not assume a functional equation for the twists of the Dirichlet series. The main new ingredient is a generalization of the familiar Weil's lemma that played a prominent role in previous converse theorems.

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