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Introduction and motivation: theta functions in one variable

  • David Mumford
Chapter
Part of the Progress in Mathematics book series (PM, volume 28)

Abstract

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
then
hence, if no is chosen so that
then the inequality
shows that the series converges and that too very rapidly.

Keywords

Functional 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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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • David Mumford
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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