Abstract
This chapter presents an analysis of the cusps on Hilbert modular varieties and values of L-functions. It presents an explicit formula for φ(M,V) in terms of the triangulation of Rn−1/V generalizing Hirzebruch's formula in the case n = 2. The chapter discusses a new idea for calculating L(M, V, 1) that would lead to the same closed formula for L(M, V,1) as for φ(M, V). The idea is essentially to identify the conditionally convergent series L(M, V, 1) as a partial fraction decomposition of φ(M, V) using Euler's formula that is in some sense the case n = 1 of Hirzebruch's conjecture. The chapter discusses two geometric invariants of the cusp (M, V) that are closely related to the signature defect φ(M,V).
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