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On the space of theta functions whose levels are square-free.
- Source :
-
Lithuanian Mathematical Journal . Jan2021, Vol. 61 Issue 1, p69-86. 18p. - Publication Year :
- 2021
-
Abstract
- Hecke conjectured that an explicit set of theta series obtained from a quaternion algebra defined over ℚ ramified at a prime N is a basis of a space of holomorphicmodular forms of weight 2 for the Hecke congruence group Γ0(N). However, Eichler noticed that Hecke's conjecture is not true in general. Hence it is natural to ask the dimension of the subspace of M2(Γ0(N)) spanned by the theta series, and this question is called Hecke's basis problem, which we have shown an answer in [K. Sugiyama, On the space of theta functions for a prime level, Comment. Math. Univ. St. Pauli, 67(1):66–81, 2019]. In this paper, we generalize the results for a square-free positive integer N. [ABSTRACT FROM AUTHOR]
- Subjects :
- *THETA functions
*FUNCTION spaces
*ALGEBRA
*QUATERNIONS
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 03631672
- Volume :
- 61
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Lithuanian Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 149287580
- Full Text :
- https://doi.org/10.1007/s10986-021-09509-w