A Kummer criterion for imaginary quadratic fields

Rodney I. Yager

Compositio Mathematica (1982)

  • Volume: 47, Issue: 1, page 31-42
  • ISSN: 0010-437X

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Yager, Rodney I.. "A Kummer criterion for imaginary quadratic fields." Compositio Mathematica 47.1 (1982): 31-42. <http://eudml.org/doc/89556>.

@article{Yager1982,
author = {Yager, Rodney I.},
journal = {Compositio Mathematica},
keywords = {Bernoulli number; Kummer's criterion; p-adic L-functions; elliptic units; elliptic curves; cyclotomic fields; complex multiplication; Größencharacter; Hecke's L-function},
language = {eng},
number = {1},
pages = {31-42},
publisher = {Martinus Nijhoff Publishers},
title = {A Kummer criterion for imaginary quadratic fields},
url = {http://eudml.org/doc/89556},
volume = {47},
year = {1982},
}

TY - JOUR
AU - Yager, Rodney I.
TI - A Kummer criterion for imaginary quadratic fields
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 47
IS - 1
SP - 31
EP - 42
LA - eng
KW - Bernoulli number; Kummer's criterion; p-adic L-functions; elliptic units; elliptic curves; cyclotomic fields; complex multiplication; Größencharacter; Hecke's L-function
UR - http://eudml.org/doc/89556
ER -

References

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  1. [1] J. Coates and A. Wiles: Kummer's criterion for Hurwitz numbers. Algebraic Number Theory, papers contributed for the International Symposium, Kyoto1976, Japan Society for the Promotion of Science (1977) 9-23. Zbl0369.12009MR450241
  2. [2] H. Hida: Kummer's criterion for the special values of Hecke L-functions of imaginary quadratic fields and congruences among cusp forms Zbl0485.10019
  3. (to appear). [3] A. Hurwitz: Über die Entwicklungskoeffizienten der lemniskatischen Funktionen. Math. Ann.51 (1899) 196-226 (=Werke II, 342-373). JFM29.0385.02
  4. [4] N. Katz: p-adic interpolation of real analytic Eisenstein series. Ann. Math.104 (1976) 459-571. Zbl0354.14007MR506271
  5. [5] S. Lichtenbaum: On p-adic L-functions associated to elliptic curves. Invent. Math.56 (1980) 19-55. Zbl0425.12017MR557580
  6. [6] K. Ribet: A modular construction of unramified p-extensions of Q(μp). Invent. Math.34 (1976) 151-162. Zbl0338.12003
  7. [7] G. Robert: Unités elliptiques, Bull. Soc. Math. France Memoire36 (1973). Zbl0314.12006MR469889
  8. [8] A. Weil: Elliptic functions according to Eisenstein and Kronecker. Springer-Verlag, 1976. Zbl0318.33004MR562289
  9. [9] R. Yager: On two variable p-adic L-functions. Ann. Math.115 (1982) 411-449. Zbl0496.12010MR647813

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