Formes modulaires modulo 2 : L始ordre de nilpotence des op茅rateurs de Hecke

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• 作者：Jean-Louis Nicolas^a ; ^{jlnicola@in2p3.fr} ; ; Jean-Pierre Serre^b ; ^{jpserre691@gmail.com}
• 刊名：Comptes Rendus Mathematique
• 出版年：2012
• 期刊代码：64_1631073x
• 类别：mt
• 出版时间：April, 2012
• 卷：350
• 期：7-8
• 页码：343-348
• 文件大小：153 K

摘要

Let be the reduction mod 2 of the 螖 series. A modular form f modulo 2 of level 1 is a polynomial in 螖. If p is an odd prime, then the Hecke operator transforms f in a modular form which is a polynomial in 螖 whose degree is smaller than the degree of f, so that is nilpotent.

The order of nilpotence of f is defined as the smallest integer such that, for every family of g odd primes , the relation holds. We show how one can compute explicitly ; if f is a polynomial of degree d in 螖, one finds that .