Converse theorems: from the Riemann zeta function to the Selberg class

DOI10.1007/s40574-016-0085-xzbMath1407.11105arXiv1605.02354OpenAlexW2359405049MaRDI QIDQ2397728

Alberto Perelli

Publication date: 23 May 2017

Published in: Bollettino dell'Unione Matematica Italiana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.02354

zbMATH Keywords

\(L\)-functionsSelberg classconverse theorems

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Related Items (10)

Classification of \(L\)-functions of degree 2 and conductor 1 ⋮ Twists by Dirichlet characters and polynomial Euler products of \(L\)-functions ⋮ Forbidden conductors of $L$-functions and continued fractions of particular form ⋮ On the Northcott property for special values of \(L\)-functions ⋮ ON THE STANDARD TWIST OF THE -FUNCTIONS OF HALF-INTEGRAL WEIGHT CUSP FORMS ⋮ Computational Aspects of Hamburger’s Theorem ⋮ On a Hecke-type functional equation with conductor \(q=5\) ⋮ On the Rankin–Selberg convolution of degree 2 functions from the extended Selberg class ⋮ Unnamed Item ⋮ The standard twist of $L$-functions revisited

Cites Work

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• A converse theorem for \(\varGamma _0(13)\)
• On the Selberg class of Dirichlet series: Small degrees
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• Selberg’s conjectures and Artin 𝐿-functions
• On the structure of the Selberg class, VI: non-linear twists
• The Rosetta Stone of L-functions
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