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The Theory of Jacobi Forms
Values of Zeta Functions and Their Applications
Zeta functions of various sorts are all-pervasive objects in modern number theory, and an ever-recurring theme is the role played by their special values at integral arguments, which are linked inExpand
The Euler characteristic of the moduli space of curves
Let Fg 1, g> 1, be the mapping class group consisting of all isotopy classes of base-point and orientation preserving homeomorphisms of a closed, oriented surface F of genus g. Let )~(~1) be itsExpand
Traces of singular moduli
Volumes of hyperbolic three-manifolds
BY“hyperbolic 3-manifold” we will mean an orientable complete hyperbolic 3-manifold M of finite volume. By Mostow rigidity the volume of M is a topological invariant, indeed a homotopy invariant, ofExpand
Quantum modular forms
for all z ∈ H and all matrices γ = ( a b c d ) ∈ SL(2, Z), where k, the weight of the modular form, is a fixed integer. Of course, there are many variants: one can replace the group SL(2, Z) by aExpand
Vassiliev invariants and a strange identity related to the Dedekind eta-function
Abstract In this paper the “function” F(q)=∑n=0∞(1−q)(1−q2)⋯(1−qn) is studied. The series does not converge in any open set, but has well-defined values and derivatives of all orders when q is a rootExpand