Short eigenvectors and multidimensional theta functions

Ron M. Adin; Yaacov Kopeliovich

doi:10.1016/S0024-3795(96)00037-7

Short eigenvectors and multidimensional theta functions

Ron M. Adin, Yaacov Kopeliovich

Department of Mathematics

University of California at Irvine

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A certain family of symmetric matrices, with entries ±1, is known to determine all the quartic relations that hold between multidimensional theta constants. Attention is drawn here to combinatorial properties of the shortest possible quartic relations, corresponding to vectors with minimal support in a certain eigenspace of such a matrix. A lower bound for the size of the support is established, exhibiting a "phase transition" at dimension four. The multiplicity-free eigenvectors with minimal support form an interesting combinatorial design, with a rich group of symmetries.

Original language	English
Pages (from-to)	49-63
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	257
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(96)00037-7
State	Published - May 1997

Bibliographical note

Funding Information:
The aim of this paper is twofold: We would like to present a few combinatorial results regarding certain identities involving theta functions, *Research supported in part by the Israel Science Foundation, administered by the Israel Academy of Sciences and Humanities, and by an Internal Research Grant from Bar-llan University. E-mail: radin@math, biu. ac. il. tPartially supported by the Edmund Landau Center for Research in Mathematical Analysis during a visit to the Hebrew University, Jerusalem. E-maih ykopelio@math, uci. edu. LINEAR ALGEBRA AND ITS APPLICATIONS 257:49-63 (1997)

Funding

The aim of this paper is twofold: We would like to present a few combinatorial results regarding certain identities involving theta functions, *Research supported in part by the Israel Science Foundation, administered by the Israel Academy of Sciences and Humanities, and by an Internal Research Grant from Bar-llan University. E-mail: radin@math, biu. ac. il. tPartially supported by the Edmund Landau Center for Research in Mathematical Analysis during a visit to the Hebrew University, Jerusalem. E-maih ykopelio@math, uci. edu. LINEAR ALGEBRA AND ITS APPLICATIONS 257:49-63 (1997)

Funders	Funder number
Bar-Ilan University
Israel Academy of Sciences and Humanities
Israel Science Foundation

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10.1016/S0024-3795(96)00037-7

Cite this

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Short eigenvectors and multidimensional theta functions

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