Quadratic congruences for Cohen–Eisenstein series
Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 141-144
Voir la notice de l'article provenant de la source Cambridge University Press
The notion of quadratic congruences was introduced in the recently published paper [A. Balog, H. Darmon and K. Ono, Congruences for Fourier coefficients of half-integral weight modular forms and special values of L-functions, in Analytic Number Theory, Vol. 1, Progr. Math.138 (Birkhäuser, Boston, 1996), 105–128.]. In this note we present different, somewhat more conceptual proofs of several results from that paper. Our method allows us to refine the notion and to generalize the results quoted. Here we deal only with the quadratic congruences for Cohen–Eisenstein series. Similar phenomena exist for cusp forms of half-integral weight as well; however, as one would expect, in the case of Eisenstein series the argument is much simpler. In particular, we do not make use of techniques other than p-adic Mazur measure, whereas the consideration of cusp forms of half-integral weight involves a much more sophisticated construction. Moreover, in the case of Cohen–Eisenstein series we are able to obtain a full and exhaustive result. For these reasons we present the argument here.
GUERZHOY, P. Quadratic congruences for Cohen–Eisenstein series. Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 141-144. doi: 10.1017/S001708959997060X
@article{10_1017_S001708959997060X,
author = {GUERZHOY, P.},
title = {Quadratic congruences for {Cohen{\textendash}Eisenstein} series},
journal = {Glasgow mathematical journal},
pages = {141--144},
year = {1999},
volume = {41},
number = {1},
doi = {10.1017/S001708959997060X},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708959997060X/}
}
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