What question did this study set out to answer?

The aim is to establish conditions under which central values of twisted L-functions do not vanish simultaneously.

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May 31, 2026

Simultaneous Non-Vanishing of Central Values of Twisted Maass L -Functions

Key Points

The aim is to establish conditions under which central values of twisted L-functions do not vanish simultaneously.
Calculated moments of twisted central L-values using advanced formulas.
Applied a Waldspurger-type formula tailored for Maass cusp forms.
Utilized the Kuznetsov trace formula relevant to the Kohnen subspace.
Established a quantitative result showing simultaneous non-vanishing of central values for twisted L-functions.
Provided conditions under which quadratically twisted L-functions associated with $SL(2, \\mathbb {Z})$ and $SL(3, \\mathbb {Z})$ remain non-zero.
Demonstrated significance of the connection between the L-values and the properties of Maass cusp forms.

Abstract

Abstract In this paper, we establish a new quantitative result for the simultaneous non-vanishing of the central values of quadratically twisted L-functions associated with SL (2, Z) and SL (3, Z) Hecke–Maass cusp forms. Our main result is derived from the calculation of moments of twisted central L-values, which is accomplished through the application of a Waldspurger-type formula for Maass cusp forms and the Kuznetsov trace formula for the Kohnen subspace.

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