Nahm's Conjecture: Asymptotic Computations and Counterexamples
Number Theory
2016-09-20 v1
Abstract
We consider certain q-series depending on parameters (A,B,C), where A is a positive definite r times r matrix, B is an r-vector and C is a scalar, and ask when these q-series are modular forms. Werner Nahm conjectured a criterion for which A's can occur, in terms of torsion in the Bloch group. The conjecture was proved by Don Zagier and Michael Terhoeven for r=1. We develop their approach for r>1 and find several new examples of modular forms as well as some counterexamples to Nahm's conjecture.
Keywords
Cite
@article{arxiv.1104.4008,
title = {Nahm's Conjecture: Asymptotic Computations and Counterexamples},
author = {Masha Vlasenko and Sander Zwegers},
journal= {arXiv preprint arXiv:1104.4008},
year = {2016}
}