Applying A. G. Postnikov's Formula in Algebraic Number Fields

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Resumo

A new result has been obtained generalizing A.G. Postnikov's formula on indices for the case of a power of 2. The multiplicative structure of the reduced residue systems modulo the degree of a prime ideal is investigated. Estimates of some sums of characters in the fields of algebraic numbers are established.

Sobre autores

H. Al-Assad

Lomonosov Moscow State University

Autor responsável pela correspondência
Email: 1hbrh0@gmail.com
Rússia, Moscow

Bibliografia

  1. Постников А.Г. О сумме характеров по модулю, равного степени простого числа // Изв. АН СССР. Сер. матем. 1955. Т. 19. № 1. С. 11–16.
  2. Аль-Ассад Х. О сумме характеров по модулю, равного степени простого числа 2 // Чебышевский сб. 2022. Т. 23. № 2. С. 201–208.
  3. Elia M.J., Interlando C., Rosenbaum R. On the Structure of Residue Rings of Prime Ideals in Algebraic Number Fields. Part I: Unramified Primes // International Mathematical Forum. 2010. V. 5. № 56. С. 2795–2808.
  4. Elia M.J., Interlando C., Rosenbaum R. On the Structure of Residue Rings of Prime Ideals in Algebraic Number Fields. Part II: Ramified Primes // International Mathematical Forum. 2011. V. 6. № 12. С. 565–589.
  5. Виноградов И.М. Избранные труды . М.: Издательство Академии наук СССР, 1952. 428 с.
  6. Архипов Г.И., Карацуба А.А., Чубариков В.Н. Теория кратных тригонометрических сумм. М.: Наука; Физматлит, 1987. 368 с.

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