Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T00:41:28.121Z Has data issue: false hasContentIssue false
  • English
  • Français

van der Pol Expansions of L-Series

Published online by Cambridge University Press:  20 November 2018

David Borwein  and
Jonathan Borwein
David Borwein
Affiliation:
Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7 e-mail: dborwein@uwo.ca
Jonathan Borwein
Affiliation:
Faculty of Computer Science, Dalhousie University, Halifax, NS, B3H 1W5 e-mail: jborwein@cs.dal.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We provide concise series representations for various $\text{L}$-series integrals. Different techniques are needed below and above the abscissa of absolute convergence of the underlying $\text{L}$-series.

Keywords

11M3511M4130B50Dirichlet series integralsHurwitz zeta functionsPlancherel theoremsL-series
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 50 , Issue 1 , 01 March 2007 , pp. 11 - 23
Copyright
Copyright © Canadian Mathematical Society 2007

References

[1] Apostol, T. M., Introduction to Analytic Number Theory. Springer-Verlag, New York, 1976.Google Scholar
[2] Borwein, J.. A class of Dirichlet series integrals. Amer. Math. Monthly 114(2007), 70–76.Google Scholar
[3] Borwein, J. and Bailey, D., Mathematics by Experiment. Plausible Reasoning in the 21st Century. AK Peters, Natick, MA, 2004.Google Scholar
[4] Borwein, J. M. and Bradley, D. M., Thirty-two Goldbach variations. Int. J. Number Theory 2(2006), no. 1, 65–103.Google Scholar
[5] Borwein, J., Bailey, D., and Girgensohn, R. Experimentation in Mathematics. Computational Paths to Discovery. AK Peters, Natick, MA, 2004.Google Scholar
[6] Borwein, J. M., Bailey, D. M., and Crandall, R. E., Computational strategies for the Riemann zeta function. J. Comput. Appl. Math. 121(2000), no. 1–2, 247–296.Google Scholar
[7] Hardy, G. H. and Wright, E. M., Introduction to the Theory of Numbers. Oxford University Press, Oxford, 1985.Google Scholar
[8] Solution to AMM Problem 10939, proposed by Ivić, with his solution. Amer. Math. Monthly 110(2003), no. 9, 847–848.Google Scholar
[9] Stromberg, K. R. Introduction to Classical Real Analysis. Wadsworth, Belmont, CA, 1981.Google Scholar