Converse theorems assuming a partial euler product

A ug 2 00 4 CONVERSE THEOREMS ASSUMING A PARTIAL EULER PRODUCT

Abstract. Associated to a newform f(z) is a Dirichlet series Lf (s) with functional equation and Euler product. Hecke showed that if the Dirichlet series F (s) has a functional equation of a particular form, then F (s) = Lf (s) for some holomorphic newform f(z) on Γ(1). Weil extended this result to Γ0(N) under an assumption on the twists of F (s) by Dirichlet characters. Conrey and Farmer exten...

A pr 2 00 5 CONVERSE THEOREMS ASSUMING A PARTIAL EULER PRODUCT

Abstract. Associated to a newform f(z) is a Dirichlet series Lf (s) with functional equation and Euler product. Hecke showed that if the Dirichlet series F (s) has a functional equation of a particular form, then F (s) = Lf (s) for some holomorphic newform f(z) on Γ(1). Weil extended this result to Γ0(N) under an assumption on the twists of F (s) by Dirichlet characters. Conrey and Farmer exten...

Holographic Reduction: A Domain Changed Application and Its Partial Converse Theorems

Some Converse Limit Theorems for Exchangeable Bootstraps

The bootstrap Glivenko-Cantelli and bootstrap Donsker theorems of Giné and Zinn (1990) contain both necessary and sufficient conditions for the asymptotic validity of Efron’s nonparametric bootstrap. In the more general case of exchangeably weighted bootstraps, Praestgaard and Wellner (1993) and Van der Vaart and Wellner (1996) give analogues of the sufficiency half of the Theorems of Giné and ...

Strong converse theorems using Rényi entropies