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VIDEO LIBRARY |
Memorial Conference on Analytic Number Theory and Applications Dedicated to the 130th Anniversary of I. M. Vinogradov
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The estimates of short weighted Kloosterman sums N. K. Semenova Lomonosov Moscow State University |
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Abstract: The incomplete weighted Kloosterman sum is the exponential sum of the type $$ S(x, m;a, b) = \sum_{\substack{\nu \leqslant x\\ (\nu, m) = 1}}{ f(\nu )\exp\Big( 2\pi i \frac{a\overline{\nu} + b\nu}{m}\Big)}, $$ where In the talk, we'll speak about some new estimates for incomplete Kloosterman sums with weights for case when $$ \exp(c (\ln m)^{2/3} (\ln\ln m)^{4/3}) \leqslant x \leqslant \sqrt{m},\quad c>0. $$ The weight function [1] A.A. Karatsuba, Fractional parts of functions of a special form, Izv. Math., 59 (1995), ¹ 4, p. 721–740. [2] A.A. Karatsuba, Analogues of Kloosterman sums, Izv. Math., 59 (1995), ¹ 5, p. 971–981. [3] M.A. Korolev, Short Kloosterman sums with weights, Math. Notes, 88 (2010), ¹ 3, p. 374–385. |