3 problems

Hecke–Fricke converse theorem for degree-2 L-functions
Hecke–Fricke converse theorem. If the Dirichlet series satisfies the stated functional equation and Euler product, then it equals $L(s,f)$ for some
openFrom papersconverse-theorems l-functions modular-forms
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2
The exact failure criterion for the naive mod $\ell$ converse theorem for $\operatorname{GL}_2(\mathbb{F}_q)$
Let $\ell$ be a prime and let $q$ be a prime power. The naive converse theorem for mod $\ell$ representations of $\operatorname{GL}_2(\mathbb{F}_q)$ asks whether the relevant mod…
openFrom papersconverse-theorems finite-groups-of-lie-type modular-representations
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4
The low-degree automorphic quotient conjecture
Let $\pi_1$ and $\pi_2$ be non-isomorphic unitary cuspidal automorphic representations of $\operatorname{GL}_{d_1}(\mathbb{A}_{\mathbb{Q}})$ and…
openFrom papersautomorphic-forms converse-theorems l-functions
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2

Hecke–Fricke converse theorem for degree-2 L-functions