2016/03/12 by Paul Monsky, Monsky, Paul · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #math.NT
paper · pdf · doi:10.48550/arxiv.1603.03910
9 pages
arxiv created 2016/03/12 · arxiv updated 2016/03/15
I begin with a simple modular form motivated proof of the following: Let Cn in Z/2[[t]] be defined by Cn+4 = Cn+3 + (t4+t3+t2+t)Cn + tn(t2+t), with initial values 0, 1, t and t2 for C0, C1, C2 and C3. Then every C4m is a sum of Ck with k<4m. This, combined with earlier results, yields: If K consists of all mod 2 modular forms of level Γ0(3) annihilated by U2 and U3 +I, then K has a basis adapted (in the sense of Nicolas and Serre) to the Hecke operators T7 and T13; consequently the Hecke algebra attached to K is a power series ring in these two operators.