Algebra and number theory are two essential research areas of fundamental mathematics. These fields have important theoretical significance and research value. Therefore, it is necessary to conduct in-depth and systematic research in these fields. For example, in the past, many researchers only studied the power mean of the exponential sums for special modulo, an odd prime. Problems that are now considered are composite modulo, or the power mean of character sums for special modulo.

This Special Issue aims to focus on some classical algebra and number theory problems (e.g., modules and ideals, rings with polynomial identity, quadratic residues, primitive roots, upper bound, and mean value estimations for various exponential sums and character sums, etc). We hope that this Special Issue also highlights new research progress discussing high-th power mean of the character sums analogous to high dimensional Kloosterman sums. Moreover, submissions mentioning sharp asymptotic formulae for the power mean of the special exponential sums are encouraged.

Potential topics include but are not limited to the following:

• Modules, ideals, and rings with a polynomial identity
• Representation theory of rings and algebras
• Character sums and their various properties
• Dedekind sums and related problems
• Exponential sums and their high-th power mean
• Prime distributions
• Quadratic residues and primitive roots
• Riemann, Hurwitz, and Lerch zeta functions
• Goldbach and Waring problems