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Incomplete Kloosterman sums to prime power modules. (English) Zbl 07413777
Summary: We prove that for prime \(p,p\to +\infty\), integer \(r\geqslant 4\) and \(q = p^r\) an incomplete Kloosterman sum of length \(N\) to modulus \(q\) can be estimated non-trivially (with power-saving factor) for very small \(N\), namely, for \(N\gg (q\log q)^{1/(r-1)}\).
11L05 Gauss and Kloosterman sums; generalizations
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