Hostname: page-component-8448b6f56d-m8qmq Total loading time: 0 Render date: 2024-04-19T20:16:09.023Z Has data issue: false hasContentIssue false

On evaluation formulas for double L-values

Published online by Cambridge University Press:  17 April 2009

Hirofumi Tsumura
Affiliation:
Department of Management Informatics, Tokyo Metropolitan College, Akishima, Tokyo 196–8540, Japan e-mail: tsumura@tmca.ac.jp
Rights & Permissions [Opens in a new window]

Extract

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.

In this paper, we give some evaluation formulas for the values of double L-series of Tornheim's type, in terms of the Dirichlet L-values and the Riemann zeta values at positive integers. As special cases, these give the formulas for double L-values given by Terhune.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Arakawa, T. and Kaneko, M., ‘On multiple L-values’, J. Math. Soc. Japan (to appear).Google Scholar
[2]Bailey, D.H., Borwein, J.M. and Girgensohn, R., ‘Experimental evaluation of Euler sums’, Experiment. Math. 3 (1994), 1730.CrossRefGoogle Scholar
[3]Huard, J.G., Williams, K.S. and Nan-Yue, Z., ‘On Tornheim's double series’, Acta Arith. 75 (1996), 105117.CrossRefGoogle Scholar
[4]Matsumoto, K., ‘On Mordell-Tornheim and other multiple zeta-functions’, in Proceedings of the Session in analytic number theory and Diophantine equations (Bonn, January-June 2002), (Heath-Brown, D.R. and Moroz, B.Z., Editors), Bonner Mathematische Schriften 360 (Mathematisches Institut der Universität Bonn, Bonn, 2003), pp. 17.Google Scholar
[5]Mordell, L.J., ‘On the evaluation of some multiple series’, J. London Math. Soc. 33 (1958), 368371.CrossRefGoogle Scholar
[6]Terhune, D., Evaluations of multiple L-values, (Ph.D. Thesis) (UT-Austin, 2002).Google Scholar
[7]Terhune, D., ‘Evaluations of double L-values’, J. Number Theory 105 (2004), 275301.CrossRefGoogle Scholar
[8]Tornheim, L., ‘Harmonic double series’, Amer. J. Math. 72 (1950), 303314.Google Scholar
[9]Tsumura, H., ‘Evaluation formulas for Tornheim's type of alternating double series’, Math. Comp. 73 (2004), 251258.Google Scholar
[10]Washington, L.C., Introduction to the cyclotomic fields, (2nd ed.) (Springer-Verlag, New York, Berlin, Heidelberg, 1997).CrossRefGoogle Scholar