p -adic L -functions for elliptic curves with complex multiplication I

Pierrette Cassou-Noguès

Compositio Mathematica (1980)

  • Volume: 42, Issue: 1, page 31-56
  • ISSN: 0010-437X

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Cassou-Noguès, Pierrette. "$p$-adic $L$-functions for elliptic curves with complex multiplication I." Compositio Mathematica 42.1 (1980): 31-56. <http://eudml.org/doc/89470>.

@article{Cassou1980,
author = {Cassou-Noguès, Pierrette},
journal = {Compositio Mathematica},
keywords = {p-adic L-functions; complex multiplication; residue formula; values of L- functions; Kummer criterion},
language = {eng},
number = {1},
pages = {31-56},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {$p$-adic $L$-functions for elliptic curves with complex multiplication I},
url = {http://eudml.org/doc/89470},
volume = {42},
year = {1980},
}

TY - JOUR
AU - Cassou-Noguès, Pierrette
TI - $p$-adic $L$-functions for elliptic curves with complex multiplication I
JO - Compositio Mathematica
PY - 1980
PB - Sijthoff et Noordhoff International Publishers
VL - 42
IS - 1
SP - 31
EP - 56
LA - eng
KW - p-adic L-functions; complex multiplication; residue formula; values of L- functions; Kummer criterion
UR - http://eudml.org/doc/89470
ER -

References

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  1. [1] N. Arthaud: On Birch and Swinnerton-Dyer's conjecture for elliptic curve with complex multiplication I. Compositio Math.37 (1978) 209-232. Zbl0396.12011MR504632
  2. [2] J. Coates: p-adic L functions and Iwasawa theory in Algebraic Number Fields, editor A. Fröhlich Academic Press, 1977. MR460282
  3. [3] J. Coates and A. Wiles: On the conjecture of Birch and Swinnerton-Dyer, Inventiones Mathematicae39 (1977) 223-251. Zbl0359.14009MR463176
  4. [4] J. Coates and A. Wiles: Kummer's criterion for Hürwitz numbers. Proceedings of the International Conference on Algebraic Number Theory. Kyoto Japan 1976. Zbl0369.12009
  5. [5] J. Coates and A. Wiles: On p-adic L-functions and elliptic units. J. Austral. Math. Soc. (series A) 26 (1978) 1-25. Zbl0442.12007MR510581
  6. [6] A. Fröhlich: Formal groups. Lecture Notes in Mathematics74. Springer1968. Zbl0177.04801MR242837
  7. [7] E. Hecke: Mathematishe werke n ° 14. Eine neue Art von Zeta funktionen und ihre Beziehungen zur Verteilung der Primzahlen, Zweite Mitteilung p. 249-289. 
  8. [8] K. Iwazawa: Lectures on p-adic L-functions. Ann. of Maths Studies74. Princeton University Press, 1972. Zbl0236.12001MR360526
  9. [9] N. Katz: The Eisenstein measure and p-adic interpolation. Amer. J. Math.99, p. 238-311. Zbl0375.12022MR485797
  10. [10] N. Katz: Formal groups and p-adic interpolation, Astérisque41-42, p. 55-65. Zbl0351.14024MR441928
  11. [11] H.W. Leopoldt: Eine p-adische Theorie der Zetawerte II. J. Reine Ang. Math.274-275 (1975) 224-239. Zbl0309.12009MR379446
  12. [12] S. Lichtenbaum: On p-adic L-functions associated to elliptic curves, Inventiones Mathematicae56 (1980) 19-55. Zbl0425.12017MR557580
  13. [13] J. Lubin: One parameter formal Lie groups over p-adic integer rings. Ann. of Maths80 (1964) 464-484. Zbl0135.07003MR168567
  14. [14] J. Lubin and J. Tate: Formal complex multiplication in local fields. Ann. of Maths81 (1965) 380-387. Zbl0128.26501MR172878
  15. [15] J. Manin and S. Vishik: p-adic Hecke series for quadratic imaginary fields. Math. Sbornik24 (1974) 345-372. Zbl0329.12016
  16. [16] G. Robert: Unités elliptiques. Bull. Soc. Math. France, mémoire 36 (1973). Zbl0314.12006MR469889
  17. [ 17] G. Shimura: Introduction to the arithmetic theory of automorphic functions. Pub. Math. Soc. JapanII (1971). Zbl0221.10029MR314766
  18. [18] C.L. Siegel: Lectures on advanced analytic number theory. Tata Institute of fundamental researchBombay. Zbl0278.10001MR262150
  19. [19] J. Tate: Arithmetic of elliptic curves. Inventiones Math.23 (1974) 179-206. Zbl0296.14018MR419359
  20. [20] S. Vishik: The p-adic zeta function of an imaginary quadratic field and the Leopold regulator. Math. Sbornik102 (144) (1977) No. 2. Zbl0443.12007MR480435

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