Eisenstein Series and the trace formula for GL(2) over a Function Field

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Abstract

We write out and prove the trace formula for a convolution operator on the space of cusp forms on GL(2) over the function field F of a smooth projective absolutely irreducible curve over a finite field. The proof - which follows Drinfeld - is complete and all terms in the formula are explicitly computed. The structure of the homogeneous space GL(2, F)\GL(2,A) is studied in section 2 by means of locally free sheaves of OX-modules. Section 3 deals with the regularization and computation of the geometric terms, over conjugacy classes. Section 4 develops the theory of intertwining operators and Eisenstein Series, and the trace formula is proven in section 5.

Original languageEnglish
Pages (from-to)1-62
Number of pages62
JournalDocumenta Mathematica
Volume19
Issue number1
StatePublished - 2014

Keywords

  • Automorphic representations, GL(2)
  • Eisenstein series
  • Function fields
  • Intertwining operators
  • Orbital integrals
  • Trace formula

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