Analysis Mathematica· 2026Q2
Sums of products of Kloosterman sums to prime power moduli
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- Q2SCImago
- 2026year
Short summary
New bounds are established for complete sums of products of k additively shifted Kloosterman sums to odd prime power moduli q=p^n, showing stronger power savings (q^{-1/⌈k/2⌉}) and quantifying shift alignment.
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Key points
- New bounds derived for complete sums of products of k additively shifted Kloosterman sums.
- Bounds apply to odd prime power moduli q=p^n.
- Achieved power savings of approximately q^{-1/⌈k/2⌉}.
- Introduced a novel quantification of alignment among shifts.
- Method based on estimating exponential sums with phases controlled by p-adic differentiability.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We prove new bounds on complete sums of products of $$k$$ k additively shifted Kloosterman sums to odd high prime power moduli $$q=p^n$$ q = p n , which feature substantially stronger power savings (about $$q^{-1/\lceil k/2\rceil}$$ q - 1 / ⌈ 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.
The authors' abstract, as published at the source. Analysis Mathematica, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics