On Riemann type relations for theta functions on bounded symmetric domains of type $I$

Atsuhira Nagano

doi:10.1016/j.laa.2023.05.003

On Riemann type relations for theta functions on bounded symmetric domains of type $I$

Number Theory 2023-05-25 v2

Authors: Atsuhira Nagano

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Abstract

We provide a practical technique to obtain plenty of algebraic relations for theta functions on the bounded symmetric domains of type $I$ . In our framework, each theta relation is controlled by combinatorial properties of a pair $(T,P)$ of a regular matrix $T$ over an imaginary quadratic field and a positive-definite Hermitian matrix $P$ over the complex number field.

Keywords

theta functions bounded symmetric domains type i algebraic relations regular matrix hermitian matrix

Cite

@article{arxiv.2301.09243,
  title  = {On Riemann type relations for theta functions on bounded symmetric domains of type $I$},
  author = {Atsuhira Nagano},
  journal= {arXiv preprint arXiv:2301.09243},
  year   = {2023}
}

Comments

16 pages, typos are corrected, unclear descriptions are corrected, abstract is revised

On Riemann type relations for theta functions on bounded symmetric domains of type $I$

Abstract

Keywords

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