Character sums to prime power moduli evaluated at binary quadratic forms

2025/08/15 by Stephan Baier, Baier, Stephan, Aishik Chattopadhyay +1
Mathematics · #11E08 #11L07 #11L40 #11T24 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.11231

openalex publication_date 2025/08/15 · openalex created_date 2026/04/25 · openalex updated_date 2026/07/28

Abstract

We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms. This complements estimates established by Heath-Brown for such character sums to squarefree moduli. Our approach uses p-adic analysis. More precisely, we use tools from the p-adic theory of exponential sums, as initiated by Milićević.

Citations

• Small solutions of generic ternary quadratic congruences to general moduli

Related

• Character Sums Over The Prime Numbers
• Bounds on short character sums and L-functions for characters with a smooth modulus
• Short character sums for composite moduli
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