Introduction and motivation: theta functions in one variable
Part of the Progress in Mathematics book series (PM, volume 28)
The central character in our story is the analytic function ϑ(z, τ) in 2 variables defined by
where z є ℂ and τ є H, the upper half plane Im τ > 0. It is immediate that the series converges absolutely and uniformly on compact sets; in fact, if
hence, if no is chosen so that
then the inequality
shows that the series converges and that too very rapidly.
KeywordsFunctional Equation Entire Function Meromorphic Function Modular Form Theta Function
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer Science+Business Media New York 1983