Multiple exponential sums and their applications to quadratic congruences

Nilanjan Bag, Stephan Baier and Anup Haldar

Mathematische Nachrichten, 2025, vol. 298, issue 11, 3599-3612

Abstract: In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables, which complements work by T. Cochrane and Z. Zheng on the single variable case. As an application, for n≥3$n\ge 3$, a fixed natural number, we obtain an asymptotic formula for the (weighted) number of solutions of general quadratic congruences modulo pm$p^m$ in small boxes, thus establishing an equidistribution result for these solutions.

Date: 2025
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