D. R. Heath-Brown

Publications101
h-index27
Citations2,584
Highly Influential Citations268
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An Introduction to the Theory of Numbers, Sixth Edition
Read more and get great! That's what the book enPDFd an introduction to the theory of numbers 5th edition will give for every reader to read this book. This is an on-line book provided in this… Expand
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Prime numbers in short intervals and a generalized Vaughan identity
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Integer Sets Containing No Arithmetic Progressions
lfh and k are positive integers there exists N(h, k) such that whenever N ^ N(h, k), and the integers 1,2,...,N are divided into h subsets, at least one must contain an arithmetic progression of… Expand
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Fractional Moments of the Riemann Zeta‐Function
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The density of rational points on cubic surfaces
NF (P ) = N(P ) = #{x ∈ Z4 : F (x) = 0, |x| ≤ P}, where |x| is the Euclidean length of x. This paper is concerned with the behaviour of N(P ) as P tends to infinity. It is clear that if the surface F… Expand
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The size of Selmer groups for the congruent number problem, II
where Np is the number of solutions of the congruence y ≡ x −D2x (mod p). Then LD(s) has an analytic continuation as an entire function on the complex plane. The conjecture of Birch and… Expand
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The Fourth Power Moment of the Riemann Zeta Function
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Cubic forms in 14 variables
The result can be rephrased in geometric language to say that any projective cubic hypersurface defined over Q, of dimension at least 12, has a Q-point. Davenport’s result was extended to arbitrary… Expand
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HYBRID BOUNDS FOR DIRICHLET L-FUNCTIONS II
for any e > 0. This estimate has had many applications, for example to sharpenings of the Brun-Titchmarsh theorem on primes in arithmetic progressions. Burgess' bound (2) is weaker than the trivial… Expand
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Weyl's Inequality, Hua's Inequality, and Waring's Problem
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