Averaging quadratically twisted L-values and their derivatives

2025/06/30 by Huang, Tinghao
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.00179

Abstract

In this paper, we unconditionally establish an asymptotic formula for the product of the quadratically twisted central L-value associated to a holomorphic cusp form f, and the quadratically twisted central L-derivative to a distinct holomorphic cusp form g. This result may be viewed as an extension of \citeLi-MR4768632, \citeKumar.etc-MR4765788 and \citezhou2025momentderivativesquadratictwists.

Citations

• Moment of Derivatives of Quadratic Twists of Modular L-Functions
• Moments of derivatives of modular L-functions
• Moments of quadratic twists of modular L-functions
• Nonvanishing of Quadratic Dirichlet L-Functions at S = &#189
• Determination of modular forms by twists of critical L-values

Related

• Determination of \textrmGL(3) cusp forms by central values of quadratic twisted L-functions
• Determination of a pair of newforms from the product of their twisted central values
• Moment of derivatives of L-functions for two distinct newforms
• Central values of additive twists of cuspidal L-functions
• The first moment of cusp form L-functions in weight aspect on average