Asymptotic distribution of sums of Rademacher functions

The Asymptotic Distribution of Exponential Sums, I

On the Asymptotic Distribution of Certain Sums

on direct sums of baer modules

the notion of baer modules was defined recently

Rademacher sums, Moonshine and Gravity

In 1939 Rademacher demonstrated how to express Klein’s modular invariant as a sum over elements of the modular group. In this article we generalize Rademacher’s approach so as to construct bases for the spaces of automorphic integrals of arbitrary even integer weight, for an arbitrary group commensurable with the modular group. Our methods provide explicit expressions for the Fourier expansions...

Asymptotic Variation of L Functions of One-variable Exponential Sums

Fix an integer d ≥ 3. Let A be the dimension-d affine space over the algebraic closure Q of Q, identified with the coefficient space of degree-d monic polynomials f(x) in one variable x. For any f(x) in A(Q), let Q(f) be the field generated by coefficients of f in Q. For each prime p coprime to d, pick an embedding from Q to Qp, once and for all. Let P be the place in Q(f) lying over p specifie...