Exponential sums and character sums play vital roles in the analytic number theory studies. Many famous number theory problems are closely related to them. Therefore, it is necessary to conduct in-depth research in these fields.

In the past, many people only studied the power mean of the exponential sums for the prime modulo p. The issue now considered is the power mean problem of the composite modulo q. Some scholars have previously studied the fourth power mean of the exponential sum and character sums. Nowadays, we consider the more general 2k-th power mean with k≥ 3.

The aim of this special issue is to solicit original research articles, as well as review articles, obtaining some exact calculating formulas or sharp asymptotic formulas for the high-th power mean of various exponential sums and character sums. This special issue also hopes to focus on the upper bound estimation, and recurrence properties. Furthermore, submissions addressing the high-th power mean of various exponential sums, the upper bound estimation, application of character sums, and the mean value of the Dedekind sums are also welcome.

Potential topics include but are not limited to the following:

• Gauss sums and Kloosterman sums
• Exponential sums and its power mean
• Upper bound estimations and applications of character sums
• Sums over primes
• Dedekind sums
• Primitive roots and k-th residues
• Hurwitz and Lerch zeta functions
• Other Dirichlet series and zeta functions