Canonical periods and congruence formulae

Duke Mathematical Journal

Volumn 98, Issue 2, 1999, Pages 397-419

  Vatsal, V ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033147842     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-99-09811-3     Document Type: Article

References (35)

1. A. Ash and G. Stevens, Modular forms in characteristic I and special values of their L-functions, Duke Math. J. 53 (1986), 849-868.
2. S. Bloch and K. Kato, “L-functions and Tamagawa numbers of motives” in The Grothendieck Festschrift, Vol. 1, Progr. Math. 86, Birkhauser, Boston, 1990, 333-400.
3. H. Carayol, Sur les représentations 1-adiques attachées aux formes modulaires de Hilbert, Ann. Sci. École Norm. Sup. (4) 19 (1986), 409-468.
4. J. Coates, “Motivic p-adic L-functions” in L -Functions and Arithmetic (Durham, 1989), London Math. Soc. Lecture Note Ser. 153, Cambridge Univ. Press, Cambridge, 1991, 141-172.
5. J. Cremona, Algorithms for Modular Elliptic Curves, Cambridge Univ. Press, Cambridge, 1992.
6. H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields, II, Proc. Roy. Soc. London. Ser. A 322 (1971), 405-420.
7. F. Diamond and J. Im, “Modular forms and modular curves” in Seminar on Fermat's Last Theorem (Toronto, 1993-1994), CMS Conf. Proc. 17 Amer. Math. Soc., Providence, 1995, 39-133.
8. G. Faltings and B. Jordan, Crystalline cohomology and GL2 (Q), Israel J. Math. 90 (1995), 1-66.
9. G. Frey, On the Selmer groups of twists of elliptic curves with Q-rational torsion points, Canad. J. Math. 40 (1988), 649-665.
10. D. Goldfeld, “Conjectures on elliptic curves over quadratic fields” in Number Theory, Carbondale 1979, Lecture Notes in Math. 751, Springer-Verlag, Berlin, 1979, 108-118.
11. R. Greenberg, “Iwasawa theory for p-adic representations” in Algebraic Number Theory, Adv. Stud. Pure Math. 17, Academic Press, Boston, 1989, 97-137.
12. R. Greenberg and G. Stevens, p-adic L-functions and p-adic periods of modular forms, Invent. Math. 111 (1993), 407-447.
13. H. Hida, Congruences of cusp forms and special values of their zeta functions, Invent. Math. 63 (1981), 225-261.
14. p [[X]]) attached to ordinary cusp forms, Invent. Math. 85 (1986), 545-613.
15. H. Iwaniec, On the order of vanishing of modular L -functions at the critical point, Sém. Théor. Nombres Bordeaux (2) 2 (1990), 365-376.
16. K. James, L-series with nonzero central critical value, J. Amer. Math. Soc. 11 (1998), 635-641.
17. W. Kohnen, On the proportion of quadratic twists of modular forms nonvanishing at the central critical point, preprint, 1997.
18. B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Éudes Sci. Publ. Math. 47 (1977), 33-186.
19. B. Mazur, On the arithmetic of special values of L-functions, Invent. Math. 55 (1979), 207-240.
20. B. Mazur, J. Tate, and J. Teitelbaum, On p-adic analogs of the conjectures of Birch and Swinnerton-Dyer, Invent. Math. 84 (1986), 1-48.
21. B. Mazur and A. Wiles, On p-adic analytic families of Galois representations, Com-postio Math. 59 (1986), 231-264.
22. M. R. Murty and V. K. Murty, Mean values of derivatives of modular L -series, Ann. of Math. (2) 133 (1991), 447-75.
23. J. Nakagawa and K. Horie, Elliptic curves with no torsion points, Proc. Amer. Math.Soc. 104 (1988), 20-24.
24. J. Nekovár, Class numbers of quadratic fields and Shimura's correspondence, Math. Ann. 287 (1990), 577-594.
25. K. Ono and C. Skinner, Fourier coefficients of half-integral weight forms modulo I, Ann. of Math. (2) 147 (1988), 453-470.
26. K. Ono and C. Skinner, Nonvanishing of quadratic twists of modular L-functions, preprint.
27. K. Rubin and A. Wiles, “Mordell-Weil groups of elliptic curves over cyclotomic fields” in Number Theory Related to Fermat's Last Theorem (Cambridge, Mass., 1981), Progr. Math. 26, Birkhauser, Boston, 1982, 237-254.
28. G. Shimura, The special values of zeta functions associated with cusp forms, Comm. Pure Appl. Math. 29 (1976), 783-804.
29. G. Stevens, Arithmetic on Modular Curves, Progr. Math. 20, Birkhauser, Boston, 1982.
30. G. Stevens, The cuspidal group and special values of L-functions, Trans. Amer. Math. Soc. 291 (1985), 519-550.
31. G. Stevens, “The Eisenstein measure and real quadratic fields” in Théorie des nombres, (Québec, PQ, 1987), de Gruyter, Berlin, 1989, 887-927.
32. p -extension, Invent. Math. 49 (1978), 87-97.
33. A. Wiles, On ordinary X-adicrepresentations associated to modular forms, Invent. Math. 94 (1988), 529-573.
34. A. Wiles, Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995), 443-551.
35. S. Wong, Elliptic curves of rank zero, preprint.