| Abstract: | The mean square of all DirichletL-functions (modq), in the form (2.1) given below, will be investigated. We establish full asymptotic expansions for (2.1) (see Theorems 1
and 2) by introducing the Mellin-Barnes type of integral formula (3.4) for the infinite double sum (3.2). Our treatment of
(2.1) becomes, by virtue of (3.4), considerably simpler than the existing methods. Further improvments (Theorems A and B)
are also given.
Research supported by Grant-in-Aid for Scientific Research (No. 07740035), Ministry of Education, Science, Sports, and Culture,
Japan.
Department of Mathematics and Computer Science, Kagoshima University, Korimoto, Kagoshima 890–0065, Japan. Published in Lietuvos
Matematikos Rinkinys, Vol. 38, No. 1, pp. 98–112, January–March, 1998. |
