Formes modulaires modulo 2 : l'ordre de nilpotence des opérateurs de Hecke

Details Formes modulaires modulo 2 : l'ordre de nilpotence des opérateurs de Hecke Formes modulaires modulo 2 : l'ordre de nilpotence des opérateurs de Hecke

2012-04-04

arxiv.org/abs/1204.1036v1

C. R. Acad. Sci. Paris, Ser. I 350 (2012)

Mathematics

Number Theory

http://dx.doi.org/10.1016/j.crma.2012.03.013

Scientific paper

The nilpotence order of the mod 2 Hecke operators. Let $\Delta=\sum_{m=0}^\infty q^{(2m+1)^2} \in F_2[[q]]$ be the reduction mod 2 of the $\Delta$ series. A modular form f modulo 2 of level 1 is a polynomial in $\Delta$. If p is an odd prime, then the Hecke operator Tp transforms f in a modular form Tp(f) which is a polynomial in $\Delta$ whose degree is smaller than the degree of f, so that Tp is nilpotent. The order of nilpotence of f is defined as the smallest integer g = g(f) such that, for every family of g odd primes p1, p2, ..., pg, the relation Tp1Tp2... Tpg (f) = 0 holds. We show how one can compute explicitly g(f); if f is a polynomial of degree d in $\Delta$, one finds that g(f) << d^(1/2).

Affiliated with

Also associated with

No associations

Rating

Formes modulaires modulo 2 : l'ordre de nilpotence des opérateurs de Hecke does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Formes modulaires modulo 2 : l'ordre de nilpotence des opérateurs de Hecke, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Formes modulaires modulo 2 : l'ordre de nilpotence des opérateurs de Hecke will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-32899