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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 $$N\gg (q\log q)^{1/(r-1)}$$.
MSC:
 11L05 Gauss and Kloosterman sums; generalizations
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References:
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