TY - JOUR
T1 - Symmetrization of the Hurwitz zeta function and Dirichlet <em>L</em> functions
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
JO - PROC R SOC A
SP - 281
LP - 301
M3 - 10.1098/rspa.2006.1762
VL - 463
IS - 2077
AU - McPhedran, Ross C
AU - Botten, Lindsay C
AU - Nicorovici, Nicolae-Alexandru P
AU - John Zucker, I
Y1 - 2007/01/08
UR - http://rspa.royalsocietypublishing.org/content/463/2077/281.abstract
N2 - 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.
ER -