D. R. Heath-Brown

activity

20022022

most citedPair Correlation for Fractional Parts of

α n^{2}

54 citations · 241 across the 42 of their papers we have counts for

collaborators

Showing 2011Show all

3 papers · 1 filter

math.NT2011

Counting rational points on smooth cyclic covers

D. R. Heath-Brown, Lillian B. Pierce

A conjecture of Serre concerns the number of rational points of bounded height on a finite cover of projective space P^{n-1}. In this paper, we achieve Serre's conjecture in the sp…

math.NT2011

Quadratic polynomials represented by norm forms

T. D. Browning, D. R. Heath-Brown

The Hasse principle and weak approximation is established for equations of the shape P(t)=N(x_1,x_2,x_3,x_4), where P is an irreducible quadratic polynomial in one variable and N i…

math.NT2011★ 5 cited

Powerfree Values of Polynomials

D. R. Heath-Brown

For irreducible integer polynomials $f (n) = n^{d} + c$ we prove an asymptotic formula for the number of $k$ -th power free values taken by $f (n)$ , for $n$ running up to $x$ , subject to th…