D. R. Heath-Brown

The density of rational points on curves and surfaces

Let

The size of Selmer groups for the congruent number problem

C

Almost-primes in arithmetic progressions and short intervals

be an irreducible projective curve of degree

The Pjateckiĭ-S̆apiro prime number theorem

d

Counting rational points on hypersurfaces

in

The Average Analytic Rank of Elliptic Curves

\mathbb{P}^3

Odd perfect numbers

, defined over

The Fourth Power Mean of Dirichlet's L-Functions

\overline{\mathbb{Q}}

Rational points on quartic hypersurfaces

. It is shown that

The circle method and diagonal cubic forms

C