Weil Converse Theorem
نویسنده
چکیده
Hecke generalized this equivalence, showing that an integral form has an associated Dirichlet series which can be analytically continued to C and satisfies a functional equation. Conversely, Weil showed that, if a Dirichlet series satisfies certain functional equations, then it must be associated to some integral form. Our goal in this paper is to describe this work. In the first three sections, we will give several definitions and useful results. In Section 4, we will discuss Hecke’s equivalence; finally, in Section 5, we will prove the Weil Converse Theorem.
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