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- Title
MEAN SQUARE OF QUADRATIC HECKE CHARACTER SUM.
- Authors
HONG ZIWEI; ZHENG ZHIYONG
- Abstract
Assuming the Generalized Riemann Hypothesis (GRH) and the Riemann Hypothesis (RH), we consider the sum S(X,Y) in the Gaussian field Q(i), where the sum is taken over all primary primes. The primary tools employed include the Poisson sum and Mellin inversion techniques. The method used in this paper differs significantly from the classical approach which relies on the partial sum method, thereby facilitating a simpler calculation within our proof. Furthermore, we present a valid asymptotic formula that is applicable when both X and Y are of comparable size.
- Subjects
RIEMANN hypothesis; PRIME numbers; GAUSSIAN distribution; POISSON algebras; MEAN square algorithms
- Publication
Journal of Mathematical Inequalities, 2023, Vol 17, Issue 2, p653
- ISSN
1846-579X
- Publication type
Article
- DOI
10.7153/jmi-2023-17-43