Hostname: page-component-6bb9c88b65-9rk55 Total loading time: 0 Render date: 2025-07-27T00:56:45.921Z Has data issue: false hasContentIssue false
  • English
  • Français

On the radius of convergence of the p-adic L-function

Published online by Cambridge University Press:  22 January 2016

Yasuo Morita
Yasuo Morita*
Affiliation:
Department of Mathematics, Hokkaido University
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 their paper [11], Kubota-Leopoldt constructed the p-adic L-function Lp(s; χ) for each Dirichlet character χ. This function Lp(s; χ) is a mero-morphic function on the open dies {|s − 1| < |<q-1 p1/(p-1)|} with a possible simple pole at s = 1.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 75 , September 1979 , pp. 177 - 193
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1979

References

[1] Amice, Y. et Fresnel, J., Fonctions zêta p-adiques des corps de nombres abéliens réels, Acta Arith., 20 (1972), 353–384.Google Scholar
[2] Cassou-Noguès, P., Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques, to appear.Google Scholar
[3] Coates, J., p-adic L functions and Iwasawa’s theory, Proceedings of the 1975 Durham Symposium, pp. 269–353. Academic Press, London-New York, 1977.Google Scholar
[4] Coates, J. and Sinnot, W., On p-adic L-functions over real quadratic fields, Inventions math., 25 (1974), 253–279.Google Scholar
[5] Coates, J. and Sinnot, W., Integrality properties of the values of partial zeta functions, Proc. London Math. Soc., 34 (1977), 365–384.Google Scholar
[6] Dedekind, R., Gesammelte mathematische Werke I—III, Braunschweig, 1930–32.Google Scholar
[7] Deligne, P. and Ribet, K., Values of abelian L-functions at negative integers, to appear.Google Scholar
[8] Fresnel, J., Nombres Bernoulli et fonctions L p-adiques, Ann. Inst. Fourier, 97 (1967), 281–333.Google Scholar
[9] Iwasawa, K., Lecture on p-adic L-functions, Ann. of Math. Studies, 74, Princeton U.P., Princeton, 1972.Google Scholar
[10] Krasner, M., Rapport sur le prolongement analytiques dans les corps values complets par la methode des éléments analytiques quasi-connexes, Bull. Soc. Math. France, Mémoire, 39–40 (1974), 131–254.Google Scholar
[11] Kubota, T. and Leopoldt, H. W., Eine p-adiche Theorie der Zetawerte, I, J. reine u. angew. Math., 214–215 (1964), 328–339.Google Scholar
[12] Leopoldt, H. W., Eine p-adische Theorie der Zetawerte, II, J. reine u. angew. Math., 274/275 (1975), 224–239.Google Scholar
[13] Morita, Y., Analytic functions on an open subsets of P1(k), to appear.Google Scholar
[14] Morita, Y., Krasner’s analytic functions and rigid analytic spaces, to appear.Google Scholar
[15] Perlis, R., On the class numbers of arithmetically equivalent fields, to appear.Google Scholar
[16] Robba, P., Fonctions analytiques sur les corps values ultramétriques complets, I, Astérisque, 10 (1973), 109–218.Google Scholar
[17] Serre, J.-P., Formes modulaires et fonctions zêta p-adiques, Lecture Notes in Math., 350 (1973), 191–268.Google Scholar
[18] Washington, L., Euler factors for p-adic L-functions, to appear.Google Scholar