Manuscript Topics

As is known to all, algebra and number theory are two important branches of basic math-ematics, whose research work has important theoretical significance and research value. Therefore, it is necessary to conduct in-depth and systematic research in these fields.

This special issue will focus on some classical algebra and number theory problems, such as modules and ideals, rings with polynomial identity, k-th residue and primitive roots, the upper bound estimate for various exponential sums and character sums, the high-th power mean of the Kloosterman sums and character sums, and so on. The project generalize and refine some of the existing results. For example, in the past many people only studied the power mean of the exponential sums for special modulo p, an odd prime. The problem now considered is for the power mean problems of composite modulo q. And some scholars have only studied the fourth power mean of the two-term exponential sums and character sums before, now we are considered the more general 2k-th power mean with k ≥ 3.

The aim of this special issue is to obtain some exact calculating formulas for the high-th power mean of some special two-term exponential sums and character sums, given some exact values for the number of the k-th residue modulo p in some special set of integers.
Potential topics include but are not limited to the following:

• Modules and ideals
• Rings with polynomial identity
• Representation theory of rings and algebras
• Kloosterman sums and its various properties
• Exponential sums and its power mean
• Upper bound estimations and applications of character sums
• Primes and related problems
• Primitive roots and k-th residues
• Riemann, Hurwitz and Lerch zeta functions
• Other Dirichlet series and zeta functions

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