A characterization of integral elliptic automorphic forms

Andrea Mori

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1994)

  • Volume: 21, Issue: 1, page 45-62
  • ISSN: 0391-173X

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Mori, Andrea. "A characterization of integral elliptic automorphic forms." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21.1 (1994): 45-62. <http://eudml.org/doc/84169>.

@article{Mori1994,
author = {Mori, Andrea},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {elliptic modular forms; derivations; -adic methods; integrality of Taylor coefficients; stiffness},
language = {eng},
number = {1},
pages = {45-62},
publisher = {Scuola normale superiore},
title = {A characterization of integral elliptic automorphic forms},
url = {http://eudml.org/doc/84169},
volume = {21},
year = {1994},
}

TY - JOUR
AU - Mori, Andrea
TI - A characterization of integral elliptic automorphic forms
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1994
PB - Scuola normale superiore
VL - 21
IS - 1
SP - 45
EP - 62
LA - eng
KW - elliptic modular forms; derivations; -adic methods; integrality of Taylor coefficients; stiffness
UR - http://eudml.org/doc/84169
ER -

References

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  2. [2] A. Grothendieck, Éléments de Géometrie Algébrique, IV. Publ. Math. IHES32, 1967. 
  3. [3] M. Harris, A note on three lemmas of Shimura. Duke Math. J.46 (1979), 871-879. Zbl0433.10016MR552530
  4. [4] M. Harris, Special values of zeta functions attached to Siegel modular forms. Ann. Sci. École Norm. Sup.14 (1981), 77-120. Zbl0465.10022MR618732
  5. [5] K. Iwasawa, Lectures on p-adic L-functions. Annals of Mathematics studies74, Princeton University Press, 1972. Zbl0236.12001MR360526
  6. [6] N. Katz, p-adic properties of modular schemes and modular forms. In " Modular Functions of One Variable III" pp. 70-189, Springer Lecture Notes in Math. 350, 1973. Zbl0271.10033MR447119
  7. [7] N. Katz, p-adic interpolation of real analytic Eisenstein series. Annals of Math.104 (1976), 459-571. Zbl0354.14007MR506271
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  10. [10] N. Katz - B. Mazur, Arithmetic moduli of elliptic curves. Annals of Math. Studies108, Princeton University Press, 1985. Zbl0576.14026MR772569
  11. [11] H. Maab, Die Differentialgleichungen in der Theorie der Siegelschen Modulfunktionen. Math. Ann.126 (1953), 44-68. Zbl0053.05602MR65584
  12. [12] J.S. Milne, Points on Shimura varieties mod p. In "Automorphic Forms, Representations, and L-functions", pp. 165-184, Proc. Sympos. Pure Math. 33-2 (1979). Zbl0418.14022MR546616
  13. [13] A. Mori, An integrality criterion for elliptic modular forms. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 9 (1990), 3-9. Zbl0702.11025MR1081819
  14. [14] A. Mori, A condition for the rationality of certain elliptic modular forms over primes dividing the level. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (9) (1990), 103-109. Zbl0744.11020MR1120129
  15. [15] A. Mori, An expansion principle for elliptic automorphic forms of quaternionic type. Preprint. 
  16. [16] M. Schlessinger, Functors of Artin rings. Trans. Amer. Math. Soc.130 (1968), 208-222. Zbl0167.49503MR217093
  17. [17] J.-P. Serre, Formes modulaires et fonctions zeta p-adiques. In "Modular Functions of One Variable III" pp. 191-268, Springer Lecture Notes in Math. 350, 1973. Zbl0277.12014MR404145
  18. [18] G. Shimura, Construction of class fields and zeta functions of algebraic curves. Annals of Math.85 (1967), 58-159. Zbl0204.07201MR204426
  19. [19] G. Shimura, Introduction to the arithmetic theory of automorphic functions. Iwanami Shoten and Princeton University Press, 1971. Zbl0221.10029MR314766

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