A supersingular congruence for modular forms

Andrew Baker

Acta Arithmetica (1998)

  • Volume: 86, Issue: 1, page 91-100
  • ISSN: 0065-1036

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Andrew Baker. "A supersingular congruence for modular forms." Acta Arithmetica 86.1 (1998): 91-100. <http://eudml.org/doc/207182>.

@article{AndrewBaker1998,
author = {Andrew Baker},
journal = {Acta Arithmetica},
keywords = {modular forms; supersingular elliptic curves},
language = {eng},
number = {1},
pages = {91-100},
title = {A supersingular congruence for modular forms},
url = {http://eudml.org/doc/207182},
volume = {86},
year = {1998},
}

TY - JOUR
AU - Andrew Baker
TI - A supersingular congruence for modular forms
JO - Acta Arithmetica
PY - 1998
VL - 86
IS - 1
SP - 91
EP - 100
LA - eng
KW - modular forms; supersingular elliptic curves
UR - http://eudml.org/doc/207182
ER -

References

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  1. [1] A. Baker, Isogenies of supersingular elliptic curves over finite fields and operations in elliptic cohomology, in preparation. 
  2. [2] D. A. Cox, z Primes of the Form x² + ny². Fermat, Class Field Theory and Complex Multiplication, Wiley, 1989. 
  3. [3] D. Husemoller, Elliptic Curves, Springer, 1987. 
  4. [4] M. Kaneko and D. Zagier, z Supersingular j-invariants, hypergeometric series, and Atkin's orthogonal polynomials, preprint. 
  5. [5] N. M. Katz, z p-adic properties of modular schemes and modular forms, in: Lecture Notes in Math. 350, Springer, 1973, 69-190. 
  6. [6] P. S. Landweber, Supersingular elliptic curves and congruences for Legendre polynomials, in: Lecture Notes in Math. 1326, Springer, 1988, 69-93. 
  7. [7] J. Lubin, J.-P. Serre and J. Tate, Elliptic curves and formal groups, mimeographed notes from the Woods Hole conference, available at http://www.ma.utexas. edu/ voloch/lst.html. 
  8. [8] G. Robert, Congruences entre séries d'Eisenstein, dans le cas supersingulier, Invent. Math. 61 (1980), 103-158. Zbl0442.10020
  9. [9] H.-G. Rück, A note on elliptic curves over finite fields, Math. Comp. 49 (1987), 301-304. Zbl0628.14019
  10. [10] J.-P. Serre, z Congruences et formes modulaires (d’après H. P. F. Swinnerton-Dyer), Sém. Bourbaki 24 e Année, 1971/2, No. 416, Lecture Notes in Math. 317, Springer, 1973, 319-338. 
  11. [11] J.-P. Serre, Formes modulaires et fonctions zêta p-adiques, Lecture Notes in Math. 350, Springer, 1973, 191-268. 
  12. [12] E. de Shalit, z Kronecker's polynomial, supersingular elliptic curves, and p-adic periods of modular curves, in: Contemp. Math. 165, Amer. Math. Soc., 1994, 135-148. Zbl0863.14015
  13. [13] J. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986. Zbl0585.14026
  14. [14] J. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179-206. Zbl0296.14018
  15. [15] J. Tate, Endomorphisms of abelian varieties over finite fields, Invent. Math. 2 (1966), 134-144. Zbl0147.20303
  16. [16] W. C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. École Norm. Sup. (4) 2 (1969), 521-560. Zbl0188.53001
  17. [17] W. C. Waterhouse and J. S. Milne, Abelian varieties over finite fields, in: Proc. Sympos. Pure Math. 20, Amer. Math. Soc., 1971, 53-64. Zbl0216.33102

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