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CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS
Author(s) -
Liu Kui,
Shparlinski Igor E.,
Zhang Tianping
Publication year - 2019
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579318000554
Subject(s) - kloosterman sum , mathematics , modulo , prime (order theory) , bilinear form , prime power , discrete mathematics , pure mathematics , arithmetic , combinatorics
We obtain a non‐trivial bound for cancellations between the Kloosterman sums modulo a large prime power with a prime argument running over very short intervals, which in turn is based on a new estimate on bilinear sums of Kloosterman sums. These results are analogues of those obtained by various authors for Kloosterman sums modulo a prime. However, the underlying technique is different and allows us to obtain non‐trivial results starting from much shorter ranges.