Periodica Mathematica Hungarica
Volume/Issue:
Volume 51: Issue 1
Divisors, spin sums and the functional equation of the Zeta-Riemann function
Author:
Michel Weber Mathématique Université Louis-Pasteur et C.N.R.S. 7 rue René Descartes 67084 Strasbourg Cedex France 7 rue René Descartes 67084 Strasbourg Cedex France

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Pages:
119–131
Online Publication Date:
17 Jan 2006
Publication Date:
13 Nov 2005
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10998-005-0024-6
Keywords:
independent spin sums; Theta function; Gamma function; Zeta-Riemann function; functional equation; divisors.
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Summary  

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $S_n$ \end{document}, \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n=1,2\dots$ \end{document} be the sequence of partial sums of independent spin random variables. We show that the distribution value of the divisors of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $S_n$ \end{document}, is intimately related to the Zeta-Riemann function via the functional equation and Theta elliptic functions.

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Cover Periodica Mathematica Hungarica
Periodica Mathematica Hungarica
Print ISSN:
0031-5303
Online ISSN:
1588-2829

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Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1971
Volumes
per Year		 2
Issues
per Year		 4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address		 H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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