Weights of modular forms on SO⁺(2,l) and congruences between Eisenstein series and cusp forms of half-integral weight on SL₂

2007/07/16 by Richard Hill, Hill, Richard
Mathematics · #11F33 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F33

paper · pdf · doi:10.48550/arxiv.0707.2365

arxiv created 2007/07/16 · arxiv updated 2009/12/01

Abstract

Let E be a level 1, vector valued Eisenstein series of half-integral weight, normalized so that the coefficients are all in ℤ. We show that there is a level one vector valued cusp form f with the same weight as E and with coefficients in ℤ, which is congruent to E modulo the constant term of E.

Related

• All modular forms of weight 2 can be expressed by Eisenstein series
• Congruences for Level 1 cusp forms of half-integral weight
• Products of Vector Valued Eisenstein Series
• Eisenstein series identities based on partial fraction decomposition
• Congruences between Hilbert modular forms of weight 2, and special values of their L-functions