Bounding $j$-invariant of integral points on $X_{\ns}^{+}(p)$

TL;DR

This paper provides explicit bounds on the $j$-invariant of integral points on the modular curve $X_{ s}^{+}(p)$ for primes $p \\ge 7$, using Baker's method to advance understanding in number theory.

Contribution

It introduces explicit bounds for the $j$-invariant of integral points on $X_{ s}^{+}(p)$, a modular curve associated with non-split Cartan subgroups, for primes $p \\ge 7$.

Findings

Derived explicit bounds depending on $p$ for the $j$-invariant.

Applied Baker's method to modular curves of level $p$.

Enhanced understanding of integral points on $X_{ s}^{+}(p)$.

Abstract

For prime $p\ge 7$, by using Baker's method we obtain two explicit bounds in terms of $p$ for the $j$-invariant of an integral point on $X_{\ns}^{+}(p)$ which is the modular curve of level $p$ corresponding to the normalizer of a non-split Cartan subgroup of $\GL_2(\Z/p\Z)$.