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P-adic interpolation of dedekind sums

Published online by Cambridge University Press:  17 April 2009

C. Snyder
C. Snyder
Affiliation:
Department of Mathematics, University of Maine, Orono, Maine 04469, United States of America
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Abstract

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In this article we give an explicit representation of p-adic Dedekind sums and their reciprocity laws by using p-adic measure theory. We then study the consequences of the p-adic reciprocity law for particular positive integer values in which case we can recover a reciprocity law for Dedekind sums attached to particular Dirichlet characters. This gives a proof different from that of Nagasaka.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 2 , April 1988 , pp. 293 - 301
Copyright
Copyright © Australian Mathematical Society 1988

References

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[3]Nagasaka, C., ‘On generalized Dedekind sums attached to Dirichlet characters’, J. Number Theory 19 (1984), 374–383.CrossRefGoogle Scholar
[4]Rosen, K. and Snyder, W., ‘p-adic Dedekind sums’, J. Reine Angew. Math. 381 (1985), 23–26.Google Scholar