Bilinear forms with Kloosterman sums and moments of twisted L-functions

2025/11/10 by Djordje Milićević, Milićević, Djordje, Qin, Xinhua +2 · 2 citations
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2511.07550

Abstract

We establish power-saving estimates for general bilinear forms with Kloosterman sums modulo arbitrary q, including when both variables are shorter than the Polya-Vinogradov range. As an application, we obtain power-saving asymptotics for the second moment of (holomorphic or Maass) modular L-functions twisted with Dirichlet characters to an arbitrary large admissible modulus q. The bounds obtained are independent of the Ramanujan-Petersson conjecture and remove all factorability conditions on q in the work of Blomer, Fouvry, Kowalski, Michel, Milicevic, and Sawin.

Citations

• Non-abelian amplification and bilinear forms with Kloosterman sums
• Modular hyperbolas and bilinear forms of Kloosterman sums
• On asymptotic formulae in some sum-product questions
• Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions
• On the exceptional zeros of Rankin-Selberg L-functions

Cited by

• Bilinear forms with Kloosterman sums via quadratic characters
• Mixed moments of twisted L-functions

Related

• Bilinear forms with Kloosterman sums via quadratic characters
• Non-abelian amplification and bilinear forms with Kloosterman sums
• Bounds for Moments of Twisted Fourier coefficients of Modular Forms
• Mixed moments of twisted L-functions
• Bilinear forms with Kloosterman and Gauss sums in function fields