TL;DR
This paper explores the foundational principles behind various aspects of theta functions and their related mathematical structures, aiming to unify their understanding while simplifying complex details.
Contribution
It proposes joint construction principles for theta functions and related structures, providing a unifying perspective in the prehistory of theta theory.
Findings
Identifies common construction principles of theta functions
Simplifies complex details in theta correspondence
Provides a unified framework for theta-related structures
Abstract
There is a huge amount of work on different kinds of theta functions, the theta correspondence, cohomology classes coming from special Schwartz classes via theta distribution, and much more. The aim of this text is to try to find joint construction principles while often leaving aside relevant but cumbersome details.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Identities · Algebraic structures and combinatorial models