The mollified fourth moment of Dirichlet L-functions

2025/09/29 by Peng Gao, Gao, Peng, Xiaosheng Wu +3 · 1 citation
Mathematics · #11F72 #11M06 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2509.24690

openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We prove an asymptotic formula with a power saving error term for the fourth moment of the family of Dirichlet L-functions to modulus q mollified by a Dirichlet polynomial of length q^\frac122-\ve, valid for all moduli q\not≡2 \pmod 4. This result was previously known only for restricted sets of moduli with smaller power savings. As a special case, when no Dirichlet polynomial is enclosed, this leads to a significant improvement on X. Wu's asymptotic evaluation of the fourth moment of Dirichlet L-functions at the cental point.

Citations

• Twisted fourth moment of Dirichlet L-functions to a fixed modulus
• Upper bounds for moments of Dirichlet L-functions to a fixed modulus
• High moments of theta functions and character sums
• Bounds on bilinear forms with Kloosterman sums
• The fourth moment of Dirichlet L-functions at the central value
• A quadratic divisor problem and moments of the Riemann zeta-function
• Extreme values of zeta and L-functions
• Applications of the<i>L</i>-functions ratios conjectures
• Integral moments of L-functions
• Integral moments of L-functions

Cited by

• Mixed moments of twisted L-functions

Related

• The fourth moment of Dirichlet L-functions along the critical line
• Twisted fourth moment of Dirichlet L-functions to a fixed modulus
• The fourth moment of Dirichlet L-functions at the central value
• Mollification of the Fourth Moment of Dirichlet L-functions
• The fourth moment of Dirichlet L-functions