Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-18T13:05:19.321Z Has data issue: false hasContentIssue false

On p-adic Dedekind sums

Published online by Cambridge University Press:  22 January 2016

Aichi Kudo*
Affiliation:
Department of Mathematics, Faculty of Liberal Arts, Nagasaki University, Bunkyo-machi, Nagasaki 852, Japan
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.

For positive integers h, k and m, the higher-order Dedekind sums are defined by

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

[ 1 ] Apostol, T. M., Generalized Dedekind sums and transformation formulae of certain Lambert series, Duke Math. J., 17 (1950), 147157.CrossRefGoogle Scholar
[ 2 ] Carlitz, L., Some theorems on generalized Dedekind sums, Pacific J. Math., 3 (1953), 513522.Google Scholar
[ 3 ] Lang, H., Uber Anwendungen höherer Dedekindscher Summen auf die Struktur elementar-arithmetischer Klassenivarianten reell-quadratischer Zahlkörper, J. reine angew. Math., 254 (1972), 1732.Google Scholar
[ 4 ] Lang, S., Cyclotomic fields, Springer-Verlag, New York, 1978.CrossRefGoogle Scholar
[ 5 ] Lang, S., Cyclotomic fields II, Springer-Verlag, New York, 1980.Google Scholar
[ 6 ] Rosen, K. H. and Snyder, W. M., p-adic Dedekind sums, J. reine angew. Math., 361 (1985), 2326.Google Scholar
[ 7 ] Shiratani, K., On Euler numbers, Mem. Fac. Sci., Kyushu Univ., 27 (1973), 15.Google Scholar
[ 8 ] Shiratani, K. and Yamamoto, S., On a p-adic interpolation function for the Euler numbers and its derivatives, Mem. Fac. Sci., Kyushu Univ., 39 (1985), 113125.Google Scholar
[ 9 ] Uehara, T., On p-adic continuous functions determined by the Euler numbers, Rep. Fac. Sci. Engrg., Saga Univ., 8 (1980), 18.Google Scholar