Character sums of composite moduli and hybrid subconvexity

2014/09/12 by Roman Holowinsky, Holowinsky, Roman, Ritabrata Munshi +3
Mathematics · #11M06 #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1409.3797

openalex publication_date 2014/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M=M₁ M₂ M₃ be the product of three distinct primes and let χ=χ₁ χ₂ χ₃ be a Dirichlet character of modulus M such that each χ_i is a primitive character modulo M_i for i=1,2,3. In this paper, we provide a δ-symbol method for obtaining non-trivial cancellation in smooth character sums of the form ∑_n=1^∞ χ(n) W(n/N), with N roughly of size √ M and W a smooth compactly supported weight function on (0, ∞). As a corollary, we establish hybrid subconvexity bounds for the associated Dirichlet L-function.

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