2011/03/01 by Kimball Martin, KIMBALL MARTIN, Mark McKee +3 · 8 citations
Mathematics · #Analytic and geometric function theory #Compact Riemann surface #Geodesic #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Laplace operator #Riemann surface #Surface (topology) #TRACE (psycholinguistics) #math.DG #math.NT
paper · pdf · doi:10.1142/s1793042111004101
published in International Journal of Number Theory 07(02), 389-429 (World Scientific) · 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
openalex publication_date 2011/03/01 · arxiv created 2015/04/22 · arxiv updated 2015/04/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.