A conjectural extension of Hecke's converse theorem

DOI10.1007/s11139-017-9953-yzbMath1443.11034arXiv1704.02570OpenAlexW3105893052MaRDI QIDQ1633163

Jonathan W. Bober, Raphael S. Steiner, Giuseppe Molteni, Sandro Bettin, Min Lee, Andrew R. Booker, Thomas Oliver, David J. Platt, John Brian Conrey

Publication date: 19 December 2018

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.02570

zbMATH Keywords

modular formsRamanujan sumsconverse theorems

Mathematics Subject Classification ID

Structure of modular groups and generalizations; arithmetic groups (11F06) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11)

Related Items

An extension of Venkatesh’s converse theorem to the Selberg class, Twisting moduli for \(\mathrm{GL}(2)\), A CONVERSE THEOREM WITHOUT ROOT NUMBERS, First moments of Rankin-Selberg convolutions of automorphic forms on \(\mathrm{GL}(2)\), ON HECKE <i>L</i>-FUNCTIONS ATTACHED TO CUSP FORMS OF HALF-INTEGRAL WEIGHT, Additive twists and a conjecture by Mazur, Rubin and Stein

Uses Software

• GAP
• SageMath

Cites Work

• A converse theorem for \(\varGamma _0(13)\)
• A note on \(\text{GL}_2\) converse theorems
• Die Untergruppen der freien Produkte von beliebigen Gruppen
• Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen
• On the Distribution of Additive Number-Theoretic Functions (II)
• An Arithmetic-Geometric Method in the Study of the Subgroups of the Modular Group
• The divisors of p ‐1
• A practical method for enumerating cosets of a finite abstract group
• Modular Forms
• Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung
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