Y. Zarhin

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20242026

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math.NT2026

Torsion points of small order on cyclic covers of $P^{1}$ . III

Boris M. Bekker, Yuri G. Zarhin

Let $d > 1$ be an integer and $K_{0}$ a perfect field such that $c ha r (K_{0})$ does not divide $d$ . Let $n > d$ be an integer that is prime to $d$ . Let $f (x) \in K_{0} [x]$ be a degree $n$ moni…

math.NT2025

Odd and Even Elliptic Curves with Complex Multiplication

Yuri G. Zarhin

We call an order $O$ in a quadratic field $K$ odd (resp. even) if its discriminant is an odd (resp. even) integer. We call an elliptic curve $E$ over the field $C$ of complex numbe…

math.NT2024

Non-isogenous superelliptic jacobians II

Yuri G. Zarhin

Let $ℓ$ be an odd prime and $K$ a field of characteristic different from $ℓ$ . Let $K ˉ$ be an algebraic closure of $K$ . Assume that $K$ contains a primitive $ℓ$ th root…

math.NT2024

Comment on "On the squarefree density of polynomials"

Yuri G. Zarhin

This is an exposition of results of R.C. Vaughan and the author (Mathematika 70 (2024), no. 4). We discuss how often the squarefree values of an integral polynomial do occur. We di…

math.NT2024

Odd quadratic orders and real $j$ -invariants

Yuri G. Zarhin

Let $O$ be an order of odd discriminant $D$ in an imaginary quadratic field $K$ . Let $C l (O)$ be the group of proper $O$ -ideals and $C l (O) [2]$ the kernel of multiplication by $2$ in…

math.NT2024

Superelliptic jacobians and central simple representations

Yuri G. Zarhin

Let f(x) be a polynomial of degree at least 5 with complex coefficients and without repeated roots. Let p be an odd prime. Suppose that all the coefficients of f(x) lie in a subfie…

Torsion points of small order on cyclic covers of P1. III

Odd and Even Elliptic Curves with Complex Multiplication

Non-isogenous superelliptic jacobians II

Comment on "On the squarefree density of polynomials"

Odd quadratic orders and real j-invariants

Superelliptic jacobians and central simple representations

Torsion points of small order on cyclic covers of $P^{1}$ . III

Odd quadratic orders and real $j$ -invariants