Vanishing periods of cusp forms over modular symbols
This paper studies the integral of a cuspidal cohomology class of an arithmetic group \(\Gamma\) over a modular symbol. A modular symbol is the image modulo \(\Gamma\) of an orbit in the appropriate symmetric space of a reductive \(\mathbb{Q}\)-subgroup \(H\) of the ambient \(\mathbb{Q}\)-group \(G\). A general formula is given for this period in terms of an adelic integral of a coefficient of the cohomology class, where we view this coefficient as an automorphic function on \(G\). Using methods from the theory of automorphic functions, we prove that these periods vanish in several infinite families of cases.
scientific article; zbMATH DE number 537279
scientific article