Twists and resonance of L-functions, II

TL;DR

This paper extends the understanding of nonlinear twists of L-functions, providing new transformation formulas and revealing resonance phenomena in classical L-functions.

Contribution

It introduces an extended transformation formula for nonlinear twists of L-functions and explores their resonance properties, advancing the analytic theory of L-functions.

Findings

Extended transformation formula relating twists with leading exponent > 1/d to dual twists

Identification of new resonance cases for classical L-functions

Development of analytic properties for new classes of nonlinear twists

Abstract

We continue our investigations of the analytic properties of nonlinear twists of L-functions developed in [4],[5] and [7]. Given an L-function of degree d, we first extend the transformation formula in [5], relating a twist with leading exponent > 1/d to its dual twist. Then we combine the results in [7] with such a transformation formula to obtain the analytic properties of new classes of nonlinear twists. This allows to detect several new cases of resonance of the classical L-functions.