Symmetrization of the Hurwitz zeta function and Dirichlet L functions

McPhedran, RC; Botten, LC; Nicorovici, NAP; John Zucker, I

Symmetrization of the Hurwitz zeta function and Dirichlet L functions

McPhedran, RC Botten, LC

Nicorovici, NAP John Zucker, I

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Publication Type:: Journal Article
Citation:: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007, 463 (2077), pp. 281 - 301
Issue Date:: 2007-01-08

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Field	Value	Language
dc.contributor.author	McPhedran, RC	en_US
dc.contributor.author	Botten, LC https://orcid.org/0000-0001-6471-6954	en_US
dc.contributor.author	Nicorovici, NAP	en_US
dc.contributor.author	John Zucker, I	en_US
dc.date.issued	2007-01-08	en_US
dc.identifier.citation	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007, 463 (2077), pp. 281 - 301	en_US
dc.identifier.issn	1364-5021	en_US
dc.identifier.uri	http://hdl.handle.net/10453/3436
dc.description.abstract	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 P and N, each of which obeys a functional equation of the Dirichlet L type, with a multiplicative factor of -1 for the functions N. 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 P and N have some of the key properties of Dirichlet L functions. © 2006 The Royal Society.	en_US
dc.relation.ispartof	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences	en_US
dc.relation.isbasedon	10.1098/rspa.2006.1762	en_US
dc.title	Symmetrization of the Hurwitz zeta function and Dirichlet L functions	en_US
dc.type	Journal Article
utslib.citation.volume	2077	en_US
utslib.citation.volume	463	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	02 Physical Sciences	en_US
utslib.for	09 Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	2077	en_US
pubs.publication-status	Published	en_US
pubs.volume	463	en_US

Abstract:

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 P and N, each of which obeys a functional equation of the Dirichlet L type, with a multiplicative factor of -1 for the functions N. 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 P and N have some of the key properties of Dirichlet L functions. © 2006 The Royal Society.

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http://hdl.handle.net/10453/3436