Binary theta functions and Borcherds products

Published 27 Nov 2022 in math.NT | (2211.14787v1)

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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