Character sums to prime power moduli evaluated at binary quadratic forms

Stephan Baier; Aishik Chattopadhyay

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arXiv · 2508.11231

Character sums to prime power moduli evaluated at binary quadratic forms

Stephan Baier·Aishik Chattopadhyay

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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 Mili\'cevi\'c.

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Stephan Baier, Aishik Chattopadhyay. 2025-08-15. Character sums to prime power moduli evaluated at binary quadratic forms. https://arxiv.org/abs/2508.11231

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