Periodic Arithmetical Functions and Gauss Sums

In this paper, we use the elementary methods and properties of classical Gauss sums to study the calculation problems of some mean values of character sums of special polynomials, and obtained several interesting calculation formulae for them. As an application, we give a criterion for determining that 2 is the cubic residue for any odd prime p.

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On the Modulus of Continuity of the Distribution of Some Arithmetical Functions

Analytic and Probabilistic Methods in Number Theory ◽

10.1515/9783112314234-025 ◽

1992 ◽

pp. 223-234 ◽

Cited By ~ 1

Keyword(s):

Modulus Of Continuity ◽

Arithmetical Functions

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A note on two-term exponential sum and the reciprocal of the quartic Gauss sums

Advances in Difference Equations ◽

10.1186/s13662-021-03353-5 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Wenpeng Zhang ◽

Xingxing Lv

Keyword(s):

Exponential Sums ◽

Exponential Sum ◽

Gauss Sums ◽

Power Mean ◽

Hybrid Power ◽

Analytic Methods ◽

Hybrid Power Mean

AbstractThe main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of quartic Gauss sums, and to give some interesting calculating formulae of them.

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On Some Rings of Arithmetical Functions

Georgian Mathematical Journal ◽

10.1515/gmj.1999.299 ◽

1999 ◽

Vol 6 (4) ◽

pp. 299-306

Author(s):

D. Bhattacharjee

Keyword(s):

Arithmetical Functions ◽

Algebraic Properties

Abstract In this paper we consider several constructions which from a given 𝐵-product *𝐵 lead to another one . We shall be interested in finding what algebraic properties of the ring 𝑅𝐵 = 〈𝐶ℕ, +, *𝐵〉 are shared also by the ring . In particular, for some constructions the rings 𝑅𝐵 and will be isomorphic and therefore have the same algebraic properties.

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