A Selberg-type zero-density result for twisted \rm GL₂ L-functions and its application

2025/05/29 by Sun, Qingfeng, Wang, Hui, Yu, Yanxue
#11F12 #11F66 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.23573

Abstract

Let f be a fixed holomorphic primitive cusp form of even weight k, level r and trivial nebentypus χ_r. Let q be an odd prime with (q,r)=1 and let χ be a primitive Dirichlet character modulus q with χ≠χ_r. In this paper, we prove an unconditional Selberg-type zero-density estimate for the family of twisted L-functions L(s, f ⊗ χ) in the critical strip. As an application, we establish an asymptotic formula for the even moments of the argument function S(t, f ⊗ χ)=π^-1arg L(1/2+ıt, f⊗χ) and prove a central limit theorem for its distribution over χ of modulus q.

Citations

• A zero-density estimate for L-functions associated with \rm GL(3) Hecke--Maass cusp forms
• New large value estimates for Dirichlet polynomials
• On the zeros of the Riemann Zeta function
• Über die Nullstellen der Riemannschen Zetafunktion

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• On a level analog of Selberg's result on S(t)
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• Exceptional zeros of Rankin-Selberg L-functions and joint Sato-Tate distributions
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