Spectra of hypergraphs and applications

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45 Scopus citations

Abstract

To a regular hypergraph we attach an operator, called its adjacency matrix, and study the second largest eigenvalue as well as the overall distribution of the spectrum of this operator. Our definition and results extend naturally what is known for graphs, including the analogous threshold bound 2 √k - 1 for k-regular graphs. As an application of our results, we obtain asymptotic behavior, as N tends to infinity, of the dimension of the space generated by classical cusp forms of weight 2 level N and trivial character which are eigenfunctions of a fixed Hecke operator Tp with integral eigenvalues.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalJournal of Number Theory
Volume60
Issue number1
DOIs
StatePublished - Sep 1996

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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