Hybrid subconvexity for class group L-functions and uniform sup norm bounds of Eisenstein series

2019/03/10 by Asbjørn Christian Nordentoft, Nordentoft, Asbjorn Christian · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1903.03932

openalex publication_date 2019/03/10 · openalex created_date 2019/03/22 · openalex updated_date 2026/07/28

Abstract

In this paper we prove a hybrid subconvexity bound for class group L-functions associated to a quadratic extension K/ℚ (real or imaginary). Our proof relies on relating the class group L-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke. The main technical contribution is the following uniform sup norm bound for Eisenstein series E(z,1/2+it)≪_ε y^1/2 (|t|+1)^1/3+ε, y≫ 1, extending work of Blomer and Titchmarsh. Finally, we propose a uniform version of the sup norm conjecture for Eisenstein series.

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• Quantum ergodicity for shrinking balls in arithmetic hyperbolic\n manifolds
• The hyperbolic circle problem over Heegner points

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