PreprintCC BY 4.0arXiv
Theta functions after Weil
Abstract
This is a mostly expository paper on the construction of theta functions on the Siegel and Hermitian half-spaces using the machinery of the Weil representation, especially theta functions weighted by polynomials. When the polynomial in question satisfies suitable homogeneity and harmonicity conditions, the resulting theta function is holomorphic. Non-holomorphic Siegel and Hermitian theta functions can be constructed in a similar way, using a more general class of polynomials.
Related
- Congruences modulo powers of 5 and 7 for the crank and rank parity functions and related mock theta-functions
- Derivatives of Theta Functions and a Problem of Lyubarskii and Nes
- Weil Operators and Remainders of Anderson Generating Functions over a Punctured Projective Line
- Bicolored Eulerian quasisymmetric functions, affine lengths, and Theta operators
- On the occurrence of congruence multiplicities between Ramanujan's theta functions
BibTeX
@misc{howard2026theta,
title = {{Theta functions after Weil}},
author = {Benjamin Howard},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13429},
eprint = {2609.13429},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13429},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Theta functions after Weil
AU - Benjamin Howard
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13429
UR - https://arxiv.org/abs/2609.13429
AB - This is a mostly expository paper on the construction of theta functions on the Siegel and Hermitian half-spaces using the machinery of the Weil representation, especially theta functions weighted by polynomials. When the polynomial in question satisfies suitable homogeneity and harmonicity conditions, the resulting theta function is holomorphic. Non-holomorphic Siegel and Hermitian theta functions can be constructed in a similar way, using a more general class of polynomials.
ER -