Binary theta functions and Borcherds products
Number Theory
2022-11-29 v1
Abstract
We obtain infinite product expansions in the sense of Borcherds for theta functions associated with certain positive-definite binary quadratic and binary hermitian forms. Among other things, we show that every weight 1 binary theta function is a Borcherds product. In particular, binary theta functions have zeros only at quadratic irrationalities.
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Cite
@article{arxiv.2211.14787,
title = {Binary theta functions and Borcherds products},
author = {Markus Schwagenscheidt and Brandon Williams},
journal= {arXiv preprint arXiv:2211.14787},
year = {2022}
}
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17 pages