# Martin Huxley

Martin Neil Huxley (born in 1944) is a British mathematician, working in the field of analytic number theory.

Martin Neil Huxley
Martin Huxley in 2008
Born1944
Alma materUniversity of Cambridge
Known forAnalytic number theory
Sieve theory
Scientific career
FieldsMathematician
InstitutionsUniversity of Cardiff

He was awarded a PhD from the University of Cambridge in 1970, the year after his supervisor Harold Davenport had died. He is a professor at Cardiff University.

Huxley proved a result on gaps between prime numbers,[1] namely that if pn denotes the n-th prime number and if θ > 7/12, then

${\displaystyle p_{n+1}-p_{n}

for all sufficiently large n.

Huxley also improved the known bound on the Dirichlet divisor problem. [2]

## References

1. ^ Huxley, M. N. (1972). "On the difference between consecutive primes". Inventiones Mathematicae. 15 (2): 164–170. doi:10.1007/BF01418933.
2. ^ Huxley, M. N. (2003). "Exponential sums and lattice points III". Proc. London Math. Soc. 87 (3): 591–609. doi:10.1112/S0024611503014485. ISSN 0024-6115. Zbl 1065.11079.