On p -adic L -functions

John Coates

Séminaire Bourbaki (1988-1989)

  • Volume: 31, page 33-59
  • ISSN: 0303-1179

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Coates, John. "On $p$-adic $L$-functions." Séminaire Bourbaki 31 (1988-1989): 33-59. <http://eudml.org/doc/110114>.

@article{Coates1988-1989,
author = {Coates, John},
journal = {Séminaire Bourbaki},
keywords = {cyclotomic fields; two-variable -adic -function; special values; complex motivic -function; pseudo-measure},
language = {eng},
pages = {33-59},
publisher = {Société Mathématique de France},
title = {On $p$-adic $L$-functions},
url = {http://eudml.org/doc/110114},
volume = {31},
year = {1988-1989},
}

TY - JOUR
AU - Coates, John
TI - On $p$-adic $L$-functions
JO - Séminaire Bourbaki
PY - 1988-1989
PB - Société Mathématique de France
VL - 31
SP - 33
EP - 59
LA - eng
KW - cyclotomic fields; two-variable -adic -function; special values; complex motivic -function; pseudo-measure
UR - http://eudml.org/doc/110114
ER -

References

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  1. 1. Bloch, S., Kato, K., p-adic étale cohomology, Publ. Math. I.H.E.S. No. 63 (1986),107-152. Zbl0613.14017MR849653
  2. 2. Cassou-Nogues, P.,Valeurs aux entiers negatifs des fonctions zêta et fonctions zêta p-adiques, Invent. Math.51 (1979),29-59. Zbl0408.12015MR524276
  3. 3. Coates, J., Flach, M.,The symmetric square of an elliptic curve, to appear. 
  4. 4. Coates, J., Perrin-Riou, B., On p-adic L-functions attached to motives over Q, Advanced Studies in Pure Math.17 (1989), 23-54. Zbl0783.11039MR1097608
  5. 5. Coates, J., On the main conjectures of Iwasawa theory, to appear in Proceedings of 1989 Durham Symposium on L-functions in Arithmetic. MR1097606
  6. 6. Coleman, R., Dilogarithms, regulators, and p-adic L-functions, Invent. Math.69 (1982), 171-208. Zbl0516.12017MR674400
  7. 7. Coleman, R., de Shalit, E., p-adic regulators on curves and special values of p-adic L-functions, Invent. Math.93 (1988), 239-266. Zbl0655.14010MR948100
  8. 8. Colmez, P., Résidu en s=1 des fonctions zeta p-adiques, Invent. Math.91 (1988), 371-389. Zbl0651.12010MR922806
  9. 9. Deligne, P., Les constantes des équations fonctionelles des fonctions L, Antwerp II,Springer L.N.349 (1973), 501-595. Zbl0271.14011MR349635
  10. 10. Deligne, P.,Valeurs de fonctions L et périodes d'intégrales, Proc. Symp. Pure Math. A.M.S.33 (1979), Vol. 2, 313-346. Zbl0449.10022MR546622
  11. 11. Deligne, P., Ribet, K., Values of abelian L-functions at negative integers over totally real fields, Invent. Math.59 (1980), 227-286. Zbl0434.12009MR579702
  12. 12. Faltings, G., p-adic Hodge theory, Journal A.M.S.1 (1988), 255-299. Zbl0764.14012MR924705
  13. 13. Ferrero, B., Greenberg, R., On the behaviour of p-adic L-functions at s=0, Invent. Math.50 (1978), 91-102. Zbl0441.12003MR516606
  14. 14. Fontaine, J-M., Messing, W., p-adic periods and p-adic etale cohomology, Contemp. Math. A.M.S.67 (1987),179-207. Zbl0632.14016MR902593
  15. 15. Gelbart, S., Jacquet, H., A relation between automorphic representations of GL(2) and GL(3), Ann. Sc. E.N.S.11 (1978),471-542. Zbl0406.10022MR533066
  16. 16. Haran, S., p-adic L-functions for modular forms, Compositio Math.62 (1987), 31-46. Zbl0618.10027MR892149
  17. 17. Iwasawa, K., On p-adic L-functions, Ann. of Math.89 (1969), 198-205. Zbl0186.09201MR269627
  18. 18. Katz, N., p-adic interpolation of real analytic Eisenstein series, Ann. of Math.104 (1976),459-571. Zbl0354.14007MR506271
  19. 19. Kubota, T., Leopoldt, H., Eine p-adische theorie der zetawerte, Crelle214/215 (1964), 328-339. Zbl0186.09103MR163900
  20. 20. Manin, J., Periods of parabolic forms and p-adic Hecke series, Math. Sbornik A.M.S.21 (1973), 371-393. Zbl0293.14008
  21. 21. Manin, J.,Values of p-adic Hecke series at integer points of the critical strip, Math. Sbornik A.M.S.22 (1974), 631-637. Zbl0304.14013
  22. 22. Manin, J., Vishik, M., p-adic Hecke series of imaginary quadratic fields, Math. Sbornik A.M.S.24 (1974), 345-371. Zbl0329.12016
  23. 23. Mazur, B., Swinnerton-Dyer, P., Arithmetic of Weil curves, Invent. Math.18 (1972), 183-266. Zbl0245.14015MR354674
  24. 24. Mazur, B., Tate, J., Teitelbaum, J., On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math.84 (1986), 1-48. Zbl0699.14028MR830037
  25. 25. Mazur, B., Wiles, A., Class fields of abelian extensions of Q , Invent. Math.76 (1984),179-330. Zbl0545.12005MR742853
  26. 26. Panciskin, A., Non-archimedean automorphic L-functions (in Russian), Moscow University (1988). Zbl0667.10017
  27. 27. Perrin-Riou, B., Points de Heegner et dérivées de fonctions L p-adiques, Invent. Math.89 (1987), 455-510. Zbl0645.14010MR903381
  28. 28. Rubin, K., Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Invent. Math.89 (1987), 527-560. Zbl0628.14018MR903383
  29. 29. Schmidt, C-G., p-adic measures attached to automorphic representations of GL(3), Invent. Math.92 (1988), 597-631. Zbl0656.10023MR939477
  30. 30. Serre, J-P., Facteurs locaux des fonctions zêta des variétés algébriques, Oeuvres, Vol.2, 581-592. 
  31. 31. Serre, J-P., Sur le r6sidu de la fonction zêta p-adique d'un corps de nombres, C.R.A.S. Paris287 (1978), 183-188. Zbl0393.12026MR506177
  32. 32. Sturm, J., Special; values of zeta functions and Eisenstein series of half integral weight, Amer. J. Math.102 (1980), 219-240. Zbl0433.10015MR564472
  33. 33. Sturm, J., Evaluation of the symmetric square at the near center point, to appear. Zbl0705.11027MR1011550
  34. 34. Wagstaff, S., The irregular primes to 125000, Math. Computation32 (1978), 583-591. Zbl0377.10002MR491465
  35. 35. Yager, R., p-adic measures on Galois groups, Invent. Math.76 (1984), 331- 343. Zbl0555.12006MR742854
  36. 36. Hida, H.,. A p-adic measure attached to the zeta functions associated with two elliptic modular forms I, Invent. Math.79 (1985), 159-195. Zbl0573.10020MR774534
  37. 37. Hida, H., p-adic L-functions for base change lifts of GL(2) to GL(3), to appear. Zbl0705.11033MR1044829

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