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On p-Adic Integration in Spaces of Modular Forms and Its Applications

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REFERENCES

  1. A. N. Andrianov, “Euler products attached to Siegel modular forms of degree 2,” Usp. Mat. Nauk, 29, 44-109 (1974).

    Google Scholar 

  2. S. Böcherer, “Über die Funktionalgleichung automorpher L-Funktionen zur Siegelschen Modul-gruppe,” J. Reine Angew. Math., 362, 146-168 (1985).

    Google Scholar 

  3. S. Böcherer and C.-G. Schmidt, ”p-Adic measures attached to Siegel modular forms,” Ann. Inst. Fourier (to appear).

  4. D. Blasius, “On the critical values of Hecke L-series,” Ann. Math. (2), 124, No.1, 23-63 (1986).

    Google Scholar 

  5. J. Coates, “On p-adic L-functions,” In: Sèminaire Bourbaki, 1987-88, No. 701, Asterisque (1989), pp. 177-178.

  6. J. Coates and B. Perrin-Riou, “On p-adic L-functions attached to motives over Q,” Adv. Stud. Pure Math., 17, 23-54 (1989).

    Google Scholar 

  7. P. Colmez, “Fonctions L p-adiques,” In: Sèminaire Bourbaki, 51ème annèe, 1998-99, No. 851 (1998).

  8. R. Coleman and B. Mazur, “The eigencurve. Galois representations in arithmetic algebraic geometry,” In: London Math. Soc. Lect. Note Ser., 254, Cambridge Univ. Press, Cambridge (1998), pp. 1-113.

    Google Scholar 

  9. P. Deligne, “Valeurs de fonctions let pèriodes d' intègrales,” In: Proc. Symp. Pure Math., Amer. Math. Soc., 33 (1979), pp. 313-342.

    Google Scholar 

  10. P. Deligne and K. A. Ribet, “Values of Abelian L-functions at negative integers over totally real elds,” Invent. Math., 59, 227-286 (1980).

    Google Scholar 

  11. S. Gelbart, I. I. Piatetski-Shapiro, and S. Rallis, Explicit Constructions of Automorphic L-Functions, Lect. Notes Math., Vol. 1254, Springer-Verlag (1987).

  12. M. Harris, “The rationality of holomorphic Eisenstein series,” Invent. Math., 63, No. 2, 305-310 (1981).

    Google Scholar 

  13. H. Hida, “A p-adic measure attached to the zeta-functions associated with two elliptic modular forms. I,” Invent. Math., 79, No. 1, 1-159 (1985).

    Google Scholar 

  14. H. Hida, “Galois representations into GL2 (Z p[[X ]])attached to ordinary cuspforms,” Invent. Math., 85, 545-613 (1986).

    Google Scholar 

  15. H. Hida, “Le produit de Petersson et de Rankin p-adique,” In: Sèminaire de Thèorie des Nombres, Paris, 1988-1989, Progr. Math., 91, Birkhäuser, Boston (1990), pp. 87-102

  16. H. Hida, “On p-adic L-functions of GL(2)×GL(2)over totally real elds,” Ann. Inst. Fourier, 40, No. 2, 311-391 (1991).

    Google Scholar 

  17. H. Hida, Elementary Theory of L-Functions and Eisenstein Series, Cambridge University Press (1993).

  18. H. Hida, ”p-Adic ordinary Hecke algebras for GL(2),” Ann. Inst. Fourier, 44, No. 5, 1289-1322 (1994).

    Google Scholar 

  19. K. Iwasawa, Lectures on p-Adic L-Functions, Ann. Math. Stud., Vol. 74, Princeton University Press (1972).

  20. N. M. Katz, ”p-Adic L-functions for CM elds,” Invent. Math., 49, No. 3, 199-297 (1978).

    Google Scholar 

  21. T. Kubota and H.-W. Leopoldt, “Eine p-adische Theorie der Zetawerte,” J. Reine Angew. Math., 214/215, 328-339 (1964).

    Google Scholar 

  22. W. Kohnen and D. Zagier, “Modular forms with rational periods,” In: Modular Forms Symp., Durham, June 30-July 10, 1983, Chichester (1984), pp. 197-249.

  23. Yu. I. Manin, “Non-Archimedean integration and Jacquet-Langlands p-adic L-functions,” Russ. Math. Surv., 31, No. 1, 5-57 (1976).

    Google Scholar 

  24. A. A. Panchishkin, Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms, Lect. Notes Math., Vol. 1471, Springer-Verlag (1991).

  25. A. A. Panchishkin, “Admissible non-Archimedean standard zeta-functions of Siegel modular forms,” In: Proc. Joint AMS Summer Conference on Motives, Seattle, July 20-August 2 1991, Vol. 2, Seattle, Providence, Rhode Island (1994), pp. 251-292.

    Google Scholar 

  26. A. A. Panchishkin, “Motives over totally real elds and p-adic L-functions,” Ann. Inst. Fourier, 44, 989-1023 (1994).

    Google Scholar 

  27. A. A. Panchishkin, “On the Siegel-Eisenstein measure and its applications,” Isr. J. Math. (to appear).

  28. A. A. Panchishkin, “Non-Archimedean Mellin transform and p-adic L-functions,” Vietnam J. Math., 3, 179-202 (1997).

    Google Scholar 

  29. I. I. Piatetski-Shapiro and S. Rallis, ”L-functions of automorphic forms on simple classical groups,” In: Modul. Forms Symp., Durham, June 30-July 10, 1983, Chichester (1984), pp. 251-261.

  30. J.-P. Serre, “Formes modulaires et fonctions zêta p-adiques,” In: Modular Functions of One Variable, Part III (Proc. Int. Summer School, Univ. Antwerp, 1972), Lect. Notes Math., Vol. 350, Springer, Berlin (1973), pp. 191-268.

    Google Scholar 

  31. G. Shimura, “On Eisenstein series,” Duke Math. J., 50, 417-476 (1983).

    Google Scholar 

  32. G. Shimura, “Eisenstein series and zeta-functions on symplectic groups,” Invent. Math., 119, No. 3, 539-584 (1995).

    Google Scholar 

  33. J. Tilouine and E. Urban, “Several variable p-adic families of Siegel-Hilbert cuspeigenforms and their Galois representations,” Ann. Sci.´Ec. Norm. Sup., 4e Sèr., 32, 499-574 (1999).

    Google Scholar 

  34. A. Wiles, “On ordinary λ-adic representations associated to modular forms,” Invent. Math., 94, No.3, 529-573 (1988).

    Google Scholar 

  35. A. Wiles, “The Iwasawa conjecture for totally real fields,” Ann. Math. (2), 131, No. 3, 493-540 (1990).

    Google Scholar 

  36. A. Wiles, “Modular elliptic curves and Fermat 's last theorem,” Ann. Math. (2), 141, No. 3, 443-455 (1995).

    Google Scholar 

  37. A. Weil, “On a certain type of characters of the idè le-class group of an algebraic number field,” In: Proc. Int. Symp. Algebraic Number Theory, Tokyo-Nikko, 1955, Tokyo (1956), pp. 1-7.

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Panchishkin, A.A. On p-Adic Integration in Spaces of Modular Forms and Its Applications. Journal of Mathematical Sciences 115, 2357–2377 (2003). https://doi.org/10.1023/A:1022875813318

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