Character sums, automorphic forms, equidistribution, and Ramanujan graphs Part II. Eigenvalues of Terras graphs

Ching Li Chai, Wen Ching Winnie Li

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6 Scopus citations

Abstract

We study two types of character sums related to Terras graphs using the method ℓ-adic cohomology. These character sums also arise as traces of Frobenii of some two dimensional linear representations of a global function field. Detailed information about these Galois representations at ramified places are obtained from analysis of vanishing cycles. Consequently we give a complete description of the automorphic forms of which these character sums appear as Fourier coefficients. These character sums are shown to be equidistributed with respect to the Sato-Tate measure.

Original languageEnglish (US)
Pages (from-to)631-661
Number of pages31
JournalForum Mathematicum
Volume16
Issue number5
StatePublished - Jan 1 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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