arXiv subjects

Michael H. Mertens

Publications and source records attributed to Michael H. Mertens.

22 records · Page 2Linked to original sources

arXiv2014

Eichler-Selberg Type Identities for Mixed Mock Modular Forms

Using holomorphic projection, we work out a parametrization for all relations of products (resp. Rankin-Cohen brackets) of weight $\tfrac 32$ mock modular forms with holomorphic shadow and weight $\tfrac 12$ modular forms in the spirit of the Kronecker-Hurwitz class number relations. In particular we obtain new proofs for several class number relations among which some are classical, others are relatively new. We also obtain similar results for the mock theta functions.

math.NT↗

arXiv2014

Asymptotic formulae for partition ranks

Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.

math.NT↗

arXiv2013

Mock Modular Forms and Class Number Relations

In this paper, we prove an almost 40 year old conjecture by H. Cohen concerning the generating function of the Hurwitz class number of quadratic forms using the theory of mock modular forms. This conjecture yields an infinite number of so far unproven class number relations.

math.NT↗

arXiv2013

Automorphism Groups of Hyperbolic Lattices

Based on the concept of dual cones introduced by J.Opgenorth we give an algorithm to compute a generating system of the group of automorphisms of a lattice endowed with a hyperbolic bilinear form.

math.NT↗