Nagoya Mathematical Journal

On $p$-adic $L$-functions and cyclotomic fields

Ralph Greenberg

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 56 (1975), 61-77.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118795272

Mathematical Reviews number (MathSciNet)
MR0360536

Zentralblatt MATH identifier
0315.12008

Subjects
Primary: 12B30
Secondary: 12A40

Citation

Greenberg, Ralph. On $p$-adic $L$-functions and cyclotomic fields. Nagoya Math. J. 56 (1975), 61--77. https://projecteuclid.org/euclid.nmj/1118795272


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References

  • [1] A. Brumer, Travaux recents dwasawa et de Leopoldt, Seminaire Bourbaki 325 (1967).
  • [2] J. Coates, S. Lichtenbaum, On -adic zeta functions, Ann. of Math., 98 (1973), 498-550.
  • [3] J. Coates, W. Sinnott, On p-adic L-functions over real quadratic fields, to appear.
  • [4] R. Greenberg, On a certain -adic representation, Inventiones Math., 21 (1973), 247-254.
  • [5] R. Greenberg, On the Iwasawa invariants of totally real number fields, to appear in Amer. J. of Math.
  • [6] K. Iwasawa, Some modules in the theory of cyclotomic fields, J. Math. Soc. Japan, 16 (1964), 42-82.
  • [7] K. Iwasawa, On p-adic L-functions, Ann. of Math., 89 (1969), 198-205.
  • [8] K. Iwasawa, Lectures on p-adic L-functions, Ann. Math. Studies 74, Princeton University Press, 1972.
  • [9] K. Iwasawa, On -extensions of algebraic number fields, Ann. of Math.,98 (1973), 246-326.
  • [10] K. Iwasawa, Computation of invariants in the theory of cyclotomic fields, J..Math. Soc. Japan, 18 (1966), 86-96.
  • [11] T. Kubota, H. Leopoldt, Eine p-adische Theorie der Zetawerte (Teil I), J. Reine Angew. Math., 213 (1964), 328-339.
  • [12] J.-P. Serre, Formes modulaires et fonctions zeta p-adiques, Proceedings of Sum- mer Institute on Modular Forms, vol. 3.
  • [13] C. L. Siegel, ber die analytische Theorie der quadratischen Formen III, Ann. of Math., 38 (1937), 212-291.
  • [14] L. Stickelberger, ber eine Verallgemeinerung der Kreistheilung, Math. Ann., 37 (1890), 321-367. University of Maryland Brandeis University

See also

  • See also: Ralph Greenberg. On $p$-adic $L$-functions and cyclotomic fields. II. Nagoya Mathematical Journal vol. 67, (1977), pp. 139-158.