112 citations · 441 across the 71 of their papers we have counts for
10 papers · 1 filter
On the distribution of Salem numbers
Friedrich Götze, Anna Gusakova
In this paper we study the problem of counting Salem numbers of fixed degree. Given a set of disjoint intervals , let $Sa…
Small Values of Indefinite Diagonal Quadratic Forms at Integer Points in at least five Variables
Paul Buterus, Friedrich Götze, Thomas Hille
For any we derive effective estimates for the size of a non-zero integral point solving the Diophantine inequality $\lvert Q[…
On points with algebraically conjugate coordinates close to smooth curves
V. Bernik, F. Götze, A. Gusakova
We show that for any sufficiently large integer and a real there exists a value such that all strips $L(Q,λ)=\{(x,y):|y-f(x)|<Q^{-λ}, x\in J=[a…
On algebraic integers in short intervals and near smooth curves
Friedrich Götze, Anna Gusakova
In 1970 A. Baker and W. Schmidt introduced regular systems of numbers and vectors, showing that the set of real algebraic numbers forms a regular system on any fixed interval. This…
Integral polynomials with small discriminants and resultants
Victor Beresnevich, Vasili Bernik, Friedrich Götze
Let be fixed, be a real parameter and denote the set of polynomials over of degree and height at most . In this paper…
Distribution of complex algebraic numbers
Friedrich Götze, Dzianis Kaliada, Dmitry Zaporozhets
For a region denote by the number of complex algebraic numbers in of degree and naive height . We show that $$ Ψ(Q;Ω)=\frac{Q^{n+…