A relative trace formula for a compact Riemann surface

Kimball Martin; Mark McKee; Eric Wambach

doi:10.1142/S1793042111004101

A relative trace formula for a compact Riemann surface

Number Theory 2015-04-23 v1 Differential Geometry

Authors: Kimball Martin , Mark McKee , Eric Wambach

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Abstract

We study a relative trace formula for a compact Riemann surface with respect to a closed geodesic $C$ . This can be expressed as a relation between the period spectrum and the ortholength spectrum of $C$ . This provides a new proof of asymptotic results for both the periods of Laplacian eigenforms along $C$ as well estimates on the lengths of geodesic segments which start and end orthogonally on $C$ . Variant trace formulas also lead to several simultaneous nonvanishing results for different periods.

Keywords

trace formula geodesics and riemannian geometry riemannian geometry

Cite

@article{arxiv.1504.05684,
  title  = {A relative trace formula for a compact Riemann surface},
  author = {Kimball Martin and Mark McKee and Eric Wambach},
  journal= {arXiv preprint arXiv:1504.05684},
  year   = {2015}
}

Comments

35 pages. This version contains minor corrections to the published version. The only change to the main results is a modification of the constants in the final theorem and corollary

A relative trace formula for a compact Riemann surface

Abstract

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