Details
| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 28 Apr 2022 |
Abstract
Keywords
- math.NT, math.AG, 11G15, 11G18, 14G35
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2022.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - Around the support problem for Hilbert class polynomials
AU - Campagna, Francesco
AU - Dill, Gabriel Andreas
PY - 2022/4/28
Y1 - 2022/4/28
N2 - Let \(H_D(T)\) denote the Hilbert class polynomial of the imaginary quadratic order of discriminant \(D\). We study the rate of growth of the greatest common divisor of \(H_D(a)\) and \(H_D(b)\) as \(|D| \to \infty\) for \(a\) and \(b\) belonging to various Dedekind domains. We also study the modular support problem: if for all but finitely many \(D\) every prime ideal dividing \(H_D(a)\) also divides \(H_D(b)\), what can we say about \(a\) and \(b\)? If we replace \(H_D(T)\) by \(T^n-1\) and the Dedekind domain is a ring of \(S\)-integers in some number field, then these are classical questions that have been investigated by Bugeaud-Corvaja-Zannier, Corvaja-Zannier, and Corrales-Rodrig\'a\~{n}ez-Schoof.
AB - Let \(H_D(T)\) denote the Hilbert class polynomial of the imaginary quadratic order of discriminant \(D\). We study the rate of growth of the greatest common divisor of \(H_D(a)\) and \(H_D(b)\) as \(|D| \to \infty\) for \(a\) and \(b\) belonging to various Dedekind domains. We also study the modular support problem: if for all but finitely many \(D\) every prime ideal dividing \(H_D(a)\) also divides \(H_D(b)\), what can we say about \(a\) and \(b\)? If we replace \(H_D(T)\) by \(T^n-1\) and the Dedekind domain is a ring of \(S\)-integers in some number field, then these are classical questions that have been investigated by Bugeaud-Corvaja-Zannier, Corvaja-Zannier, and Corrales-Rodrig\'a\~{n}ez-Schoof.
KW - math.NT
KW - math.AG
KW - 11G15, 11G18, 14G35
M3 - Preprint
BT - Around the support problem for Hilbert class polynomials
ER -