An integrality criterion for elliptic modular forms

Andrea Mori

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 1, page 3-9
  • ISSN: 1120-6330

Abstract

top
Let f be an elliptic modular form level of N. We present a criterion for the integrality of f at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to f the iterates of the Maaß differential operators.

How to cite

top

Mori, Andrea. "An integrality criterion for elliptic modular forms." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.1 (1990): 3-9. <http://eudml.org/doc/244217>.

@article{Mori1990,
abstract = {Let \( f \) be an elliptic modular form level of N. We present a criterion for the integrality of \( f \) at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to \( f \) the iterates of the Maaß differential operators.},
author = {Mori, Andrea},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Modular forms; Modular curves; Complex multiplications; elliptic modular form; Maaß operator; space of moduli of elliptic curves},
language = {eng},
month = {2},
number = {1},
pages = {3-9},
publisher = {Accademia Nazionale dei Lincei},
title = {An integrality criterion for elliptic modular forms},
url = {http://eudml.org/doc/244217},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Mori, Andrea
TI - An integrality criterion for elliptic modular forms
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/2//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 1
SP - 3
EP - 9
AB - Let \( f \) be an elliptic modular form level of N. We present a criterion for the integrality of \( f \) at primes not dividing N. The result is in terms of the values at CM points of the forms obtained applying to \( f \) the iterates of the Maaß differential operators.
LA - eng
KW - Modular forms; Modular curves; Complex multiplications; elliptic modular form; Maaß operator; space of moduli of elliptic curves
UR - http://eudml.org/doc/244217
ER -

References

top
  1. HARRIS, M., A note on three lemmas of Shimura. Duke Math. J., 46, 1979, 871-879. Zbl0433.10016MR552530
  2. HARRIS, M., Special values of zeta functions attached to Siegel modular forms. Ann. scient. Ec. Norm. Sup., IV-4, 1981, 77-120. Zbl0465.10022MR618732
  3. IGUSA, J., On the algebraic theory of elliptic modular functions. J. Math. Soc. Japan, 20, 1968, 96-106. Zbl0164.21101MR240103
  4. KATZ, N., p-adic properties of modular schemes and modular forms. In: Modular functions of one variable III. LNM, Springer, 350, 1973, 70-189. Zbl0271.10033MR447119
  5. KATZ, N., p-adic interpolation of real analytic Eisenstein series. Annals of Math., 104, 1976, 459-571. Zbl0354.14007MR506271
  6. KATZ, N., p-adic L-functions for CM fields. Inventiones Math., 49, 1981, 199-297. Zbl0417.12003MR513095DOI10.1007/BF01390187
  7. KATZ, N., Serre-Tate local moduli. In: Surfaces Algebraiques. LMN, Springer, 868, 1981, 138-202. Zbl0477.14007MR638600
  8. MAAß, H., Die Differentialgleichungen in der Théorie der Siegelschen Modulfunktionen. Math. Ann., 126, 1953, 44-68. Zbl0053.05602MR65584
  9. MORI, A., Integrality of elliptic modular forms via Maaß operators. Ph. D. thesis, Brandeis Univ., 1989. MR2637460
  10. RAMANUJAN, S., On certain arithmetical functions. Trans. Camb. Phil. Soc, 22, 1916, 159-184. 
  11. SERRE, J. P., Une interpretation des congruences relatives à la fonction τ de Ramanujan. Séminaire Delonge-Pisot-Poitou, 1967-68, exposé 14. Zbl0186.36902
  12. SERRE, J. P., Congruences et formes modulaires. Séminaire Bourbaki, exposé 416, LNM, Springer, 317, 1973. Zbl0276.14013MR466020
  13. SHIMURA, G., Introduction to the arithmetic theory of automorphic functions. Iwanami Shoten and Princeton Univ. Press, 1971. Zbl0872.11023MR314766
  14. SWINNERTON-DYER, H. P. F., On l-adic representations and congruences for coefficients of modular forms. In: Modular functions of one variable III. LNM, Springer, 350, 1973, 1-56. Zbl0267.10032MR406931

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.