RT Journal Article
SR Electronic
T1 Symmetrization of the Hurwitz zeta function and Dirichlet *L* functions
JF Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
JO PROC R SOC A
FD The Royal Society
SP 281
OP 301
DO 10.1098/rspa.2006.1762
VO 463
IS 2077
A1 McPhedran, Ross C
A1 Botten, Lindsay C
A1 Nicorovici, Nicolae-Alexandru P
A1 John Zucker, I
YR 2007
UL http://rspa.royalsocietypublishing.org/content/463/2077/281.abstract
AB We consider the Hurwitz zeta function ζ(s,a), and form two parts ζ+ and ζ− by symmetric and antisymmetric combinations of ζ(s,a) and ζ(s,1−a). We consider the properties of ζ+ and ζ−, and then show that each may be decomposed into parts denoted by and , each of which obeys a functional equation of the Dirichlet L type, with a multiplicative factor of −1 for the functions . We show the results of this procedure for rational a=p/q, with q=1, 2, 3, 4, 5, 6, 7, 8, 10, and demonstrate that the functions and have some of the key properties of Dirichlet L functions.