KCI등재
학술저널
ON THE MINUS PARTS OF CLASSICAL POINCARÉ SERIES
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 31, No. 3
- : KCI등재
- 2018.08
- 281 - 285 (5 pages)
Let Sk(N) be the space of cusp forms of weight k for Γo(N). We show that Sk(N) is the direct sum of subspaces Sk⁺((N) and Sk⁻(N). Where Sk⁺(N) is the vector space of cusp forms of weight k for the group Γo⁺(N) generated by Γo(N) and WN and Sk⁻(N) is the subspace consisting of elements f in Sk(N) satisfying f|kWN = -f. We find generators spanning the space Sk⁻(N) from Poincare series and give all linear relations among such generators.
Abstract
1. Introduction and statement of results
2. Harmonic weak Maass forms
3. Proof of Theorem 1.1
References