Symmetrization of the Hurwitz zeta function and Dirichlet
functions. (English) Zbl 1151.11342
Summary: We consider the Hurwitz zeta function , and form two parts and by symmetric and antisymmetric combinations of and . We consider the properties of and , and then show that each may be decomposed into parts denoted by and , each of which obeys a functional equation of the Dirichlet type, with a multiplicative factor of - 1 for the functions . We show the results of this procedure for rational , with , 4, 5, 6, 7, 8, 10, and demonstrate that the functions and have some of the key properties of Dirichlet functions.
|11M35||Hurwitz and Lerch zeta functions|