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# Communications in Number Theory and Physics

## Volume 4 (2010)

### Number 4

### A note on Nahm’s conjecture in rank 2 case

Pages: 609 – 622

DOI: http://dx.doi.org/10.4310/CNTP.2010.v4.n4.a1

#### Authors

#### Abstract

The aim of this paper is to get a complete list of positivedefinite symmetric matrices with integer entries$\left[\begin{smallmatrix}a &b \\ b &d\end{smallmatrix}\right]$ such that allcomplex solutions to the system of equations\begin{align}1-x_1=x_1^ax_2^b, \nonumber \\1-x_2=x_1^bx_2^d \nonumber\end{align}are real. This result is related to Nahm's conjecture in rank 2 case.