INCOMPLETE KLOOSTERMAN SUMS TO PRIME POWER MODULES

We prove that for prime p, p → +∞, integer r ≥ 4 and q = pr 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 ≫ (q log q)1/(r−1).

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Bibliographic Details
Published in:Bulletin de l'Académie serbe des sciences, Classe des sciences mathématiques et naturelles. Sciences mathématiques Classe des sciences mathématiques et naturelles. Sciences mathématiques, 2021-01 (46), p.73-92
Main Authors: KOROLEV, M.Å., REZVYAKOVA, I. S.
Format: Article
Language:English
Online Access:Get full text
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Summary:We prove that for prime p, p → +∞, integer r ≥ 4 and q = pr 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 ≫ (q log q)1/(r−1).
ISSN:0561-7332
2406-0909