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math.NT2022
Uniform Distribution of Hardy Sums
Alessandro Lägeler
We employ the spectral theory of Eisenstein series to prove that the Hardy sums, integer-valued analogs of the classical Dedekind sums, are uniformly distributed in $\mathbf{Z} / m…
math.NT2022
Cycle Integrals of the Parson Poincaré Series and Intersection Angles of Geodesics on Modular Curves
Alessandro Lägeler, Markus Schwagenscheidt
We prove a geometric formula for the cycle integrals of Parson's weight 2k modular integrals in terms of the intersection angles of geodesics on modular curves. Our result is an an…
math.NT2022
Two Geometric Interpretations of Hardy Sums
Alessandro Lägeler
The problem of finding the number of lattice points in a triangle has a classical solution if the lattice is and the vertices of the triangle have integer valued coo…