Abstract:
Using Karatsuba's method, we obtain estimates for Kloosterman sums modulo a prime, in which the number of terms is less than an arbitrarily small fixed power of the modulus. These bounds refine similar results obtained earlier by Bourgain and Garaev.
Bibliography: 16 titles.
Keywords:
short Kloosterman sums, Karatsuba's method, inverse residues.
This publication is cited in the following 16 articles:
N. K. Semenova, “On estimating an inhomogeneous Kloosterman sum by the Karatsuba method”, Math. Notes, 116:3 (2024), 527–540
Roni Con, Noah Shutty, Itzhak Tamo, Mary Wootters, “Repairing Reed-Solomon Codes Over Prime Fields via Exponential Sums”, IEEE Trans. Inform. Theory, 70:12 (2024), 8587
Roni Con, Noah Shutty, Itzhak Tamo, Mary Wootters, 2023 IEEE International Symposium on Information Theory (ISIT), 2023, 1330
Moubariz Z. Garaev, Igor E. Shparlinski, “On the distribution of modular inverses from short intervals”, Mathematika, 69:4 (2023), 1183
M. A. Korolev, “Vinogradov's sieve and an estimate for an incomplete Kloosterman sum”, Sb. Math., 213:2 (2022), 216–234
R. J. L. Oliver, K. Soundararajan, “The distribution of consecutive prime biases and sums of sawtooth random variables”, Math. Proc. Camb. Philos. Soc., 168:1 (2020), PII S0305004118000592, 149–169
M. A. Korolev, “Short Kloosterman Sums with Primes”, Math. Notes, 106:1 (2019), 89–97
M. A. Korolev, “Elementary Proof of an Estimate for Kloosterman Sums with Primes”, Math. Notes, 103:5 (2018), 761–768
M. A. Korolev, “New estimate for a Kloosterman sum with primes for a composite modulus”, Sb. Math., 209:5 (2018), 652–659
M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661
M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170
K. Gong, C. Jia, M. A. Korolev, “Shifted character sums with multiplicative coefficients, II”, J. Number Theory, 178 (2017), 31–39
M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43
M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142
M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827
M. A. Korolev, “Methods of estimating of incomplete Kloosterman sums”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 230–245
Citation in format AMSBIB
Contact us: