A RELATIVE TRACE FORMULA FOR A COMPACT RIEMANN SURFACE

作者：Martin Kimball^*; Mckee Mark; Wambach Eric

来源：International Journal of Number Theory, 2011, 7(2): 389-429.

DOI：10.1142/S1793042111004101

• Relative trace formula
• compact Riemann surface
• period integrals
• lengths of geodesics

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.

• 出版日期2011-3