Quantum $j$-Invariant in Positive Characteristic II: Formulas and Values at the Quadratics

Abstract

The multi-valued quantum $j$-invariant in positive characteristic is studied at quadratic elements. For every quadratic $f$, an explicit expression for each of the values of $j^{\mathrm{qt}}(f)$ is given as a limit of rational functions of $f$. It is proved that the number of values of $j^{\mathrm{qt}}(f)$ is finite and that none of these values is $\infty$.

8 pages

References in corpus (1)

• Quantum j-invariant in positive characteristic I: Definition and Convergence