Bound the difference of two singular moduli

Abstract

For a fixed singular modulus $\alpha$, we give an effective lower bound of norm of $x-\alpha$ for another singular modulus $x$ with large discriminant. We then generalize this result for ${\Phi }_m(x,\alpha )$, where ${\Phi }_m(X,Y)\in \mathbb{Z}[X,Y]$ is the $m$-th modular polynomial.

References in corpus (3)

• Singular Moduli that are Algebraic Units
• Six unlikely intersection problems in search of effectivity
• On singular moduli that are S-units

Cited by in corpus (1)

• Effective bounds on differences of singular moduli that are S-units