Про ефективне обчислення сум характерів на основі методів А. Г. Постнікова: Fìz.-mat. model. ìnf. tehnol. 2021, 32:13-16

• Datum: 2021
• 1. Verfasser: Glazunov, Nikolaj
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Schlagworte: характери абелевої групи; p-адична арифметика; аналіз p-адичної арифметики; сума характерів; сума Клоостермана; ефективне обчислення
• Online Zugang: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/151
• Назва журналу: Physico-mathematical modeling and informational technologies

An efficient p-adic method and the structure of an algorithm for computing the sums of characters of finite abelian groups are presented. The method and algorithm are based on the A.G. Postnikov summation method of characters modulo a prime power and its developments. A brief survey of the theory of characters of finite abelian groups, p-adic arithmetic and analysis is presented. Questions of the efficiency of p-adic methods are discussed. Moreover, we present results of computation of other types of sums of characters (Kloosterman sums), which are connecting with Artin-Schreier coverings over prime finite fields. The corresponding method and algorithm are based on the development of another method by A.G. Postnikov. Examples of computation of sums of characters are given. References Pontryagin, L. S. (1986). Continuous groups, 3rd ed. Moscow: Nauka. Postnikov, A. G. (2005). Selected Works, Moscow: Fizmatlit. Borevich, Z. I, Shafarevich, I. R. (1985). Number theory, Moscow: Nauka. Karatsuba, A. A. (1975). Fundamentals of Analytic Number Theory, Moscow: Nauka. Chubarikov, V. N. (1981). On asymptotic formulas for the integral I.M. Vinogradov and his generalizations, Tr. Steklov Mathematical Institute of the USSR, 157. Khrennikov, A. Yu., Nilsson, M. (2004). p-adic deterministic and random dynamics, Dordrecht: Kluver Academic Publ. Glazunov, N. M. (2017). Arithmetic Statistics, Probabilities and Langlands correspondence, Proc. of Int. Conf. on Analytical and Computational Methods in Probability Theory and its Applications (ACMPT-2017), Lomonosov state university. Glazunov, N. M. (2019). p-adic L-functions and p-adic multiple zeta values. Chebyshevskii Sbornik, 1, 112–130.