Sums of products of Kloosterman sums to prime power moduli

Djordje Milićević; Catherine Robinson; Chloe Shupe

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arXiv · 2608.21346

Sums of products of Kloosterman sums to prime power moduli

Djordje Milićević·Catherine Robinson·Chloe Shupe

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Abstract

We prove new bounds on complete sums of products of k additively shifted Kloosterman sums to odd high prime power moduli q=p^n, which feature substantially stronger power savings (about q^(-1/ceil(k/2)) in generic configurations) and a novel quantification of the alignment among the shifts. We prove our bounds by developing a method to estimate complete exponential sums with a broad class of phases well-controlled by a specified number of initial terms in a property reflecting p-adic differentiability.

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Djordje Milićević, Catherine Robinson, Chloe Shupe. 2026-08-21. Sums of products of Kloosterman sums to prime power moduli. https://arxiv.org/abs/2608.21346

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