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Intersecting a plane with algebraic subgroups of multiplicative groups

- E. Bombieri, D. Masser, U. Zannier
- Mathematics
- 1999

Consider an arbitrary algebraic curve defined over the field of all alge- braic numbers and sitting in a multiplicative commutative algebraic group. In an earlier article from 1999 bearing almost the… Expand

Anomalous Subvarieties—Structure Theorems and Applications

- E. Bombieri, D. Masser, U. Zannier
- Mathematics
- 2007

When a fixed algebraic variety in a multiplicative group variety is intersected with the union of all algebraic subgroups of fixed dimension, a key role is played by what we call the anomalous… Expand

Torsion anomalous points and families of elliptic curves

- D. Masser, D. Zannier
- Mathematics
- 1 May 2008

We prove that there are at most finitely many complex $\lambda \neq 0,1$ such that two points on the Legendre elliptic curve $Y^2 = X(X-1)(X-\lambda)$ with coordinates $X = 2,3$ both have finite… Expand

Counting algebraic numbers with large height II

Let ℚ denote the field of rational numbers, Open image in new window an algebraic closure of ℚ, and H : Open image in new window the absolute, multiplicative, Weil height. For each positive integer d… Expand

Uniformly counting points of bounded height

1. Introduction. In this paper we give some new uniform estimates for the cardinalities of certain sets involving algebraic numbers of bounded height. The estimates are nearly optimal with respect to… Expand

Rational values of the Riemann zeta function

- D. Masser
- Mathematics
- 1 November 2011

Abstract We prove the existence of a constant C such that for any D ⩾ 3 there are at most C ( log D log log D ) 2 rational numbers s with 2 s 3 and denominator at most D such that ζ ( s ) is also… Expand

Torsion points on families of squares of elliptic curves

- D. Masser, U. Zannier
- Mathematics
- 1 February 2012

In a recent paper we proved that there are at most finitely many complex numbers λ ≠ 0,1 such that the points $${(2,\sqrt{2(2-\lambda)})}$$ and $${(3, \sqrt{6(3-\lambda)})}$$ are both torsion on the… Expand

Linear equations over multiplicative groups, recurrences, and mixing I

- H. Derksen, D. Masser
- Mathematics
- 21 October 2010

Let u1,…,umu1,…,um be linear recurrences with values in a field KK of positive characteristic pp. We show that the set of integer vectors (k1,…,km)(k1,…,km) such that… Expand

On unlikely intersections of complex varieties with tori

- E. Bombieri, D. Masser, U. Zannier
- Mathematics
- 2008

Counting points of small height on elliptic curves

- D. Masser
- Mathematics
- 1989

— Let k be a number field and let E be an elliptic curve defined over k. We prove a counting result which gives, among other things, the existence of a positive constant C, effectively computable in… Expand

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