Evaluating Theta Derivatives with Rational Characteristics
Shaul Zemel
TL;DR
This paper evaluates 35 theta derivatives with rational characteristics using Matsuda's method, expressing their derivatives as linear combinations of known theta series, advancing computational techniques in theta function analysis.
Contribution
Introduces a systematic evaluation of multiple theta derivatives with rational characteristics using a specific method, expanding computational tools for theta functions.
Findings
Successfully evaluated 35 theta derivatives with rational characteristics.
Expressed derivatives as linear combinations of known theta series.
Enhanced computational methods for theta function derivatives.
Abstract
We evaluate 35 different theta derivatives with rational characteristics using the method of Matsuda, in which the logarithmic derivatives at of the triple product expansions of the associated theta functions become linear combinations of known theta series of weight 1.
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