D. R. Heath-Brown

发表

The Differences between Consecutive Primes

D. R. Heath-Brown, 1978 .

Every sum of cubes in F2[t] is a strict sum of 6 cubes

Luis H. Gallardo, D. R. Heath-Brown, L. Gallardo, 2007, Finite Fields Their Appl..

The Research Conference

Gerd Faltings, D. R. Heath-Brown, D. R. Heath-Brown, 1936 .

Burgess's Bounds for Character Sums

D. R. Heath-Brown, 2012, Number Theory and Related Fields.

ARTIN'S CONJECTURE FOR PRIMITIVE ROOTS

D. R. Heath-Brown, 1986 .

The Theory of the Riemann Zeta-Function

D. R. Heath-Brown, E. C. Titchmarsh, 1987 .

On the difference between consecutive primes

D. R. Heath-Brown, H. Iwaniec, Henryk Iwaniec, 1979 .

The number of primes in a short interval.

D. R. Heath-Brown, 1988 .

The density of rational points on Cayley's cubic surface

D. R. Heath-Brown, 2002, math/0210333.

Square-free values of $n^2+1$

D. R. Heath-Brown, 2010, 1010.6217.

Lattice points in the sphere

D. R. Heath-Brown, 1999 .

Integer Sets Containing No Arithmetic Progressions

D. R. Heath-Brown, 1987 .

APPLICATIONS OF SIEVE METHODS TO THE THEORY OF NUMBERS

D. R. Heath-Brown, 1980 .

An estimate for Heilbronn's exponential sum

D. R. Heath-Brown, 1996 .

On solving the diophantine equation $ x^ 3 + y^ 3 + z^ 3 = k $ on a vector computer

W. M. Lioen, H.J.J. teRiele, Walter M. Lioen, 1991 .

Arithmetic applications of Kloosterman sums

D. R. Heath-Brown, Kloosterman Centennial Celebration, 2000 .

The density of zeros of forms for which weak approximation fails

D. R. Heath-Brown, 1992 .

The distribution and moments of the error term in the Dirichlet divisor problem Acta Arith

D. R. Heath-Brown, 1992 .

On the difference between consecutive primes

Henryk Iwaniec, D. R. Heath-Brown, 1979 .

On solving the Diophantine equation ³+³+³= on a vector computer

W. M. Lioen, Walter M. Lioen, D. R. Heath-Brown, 1993 .

The density of rational points on curves and surfaces

D. R. Heath-Brown, J.-L. Colliot-Th'elene, J.-L. Colliot-Th'elene, 2002, math/0405392.

Zero-free regions for Dirichlet $L$-functions, and the least prime in an arithmetic progression

D. R. Heath-Brown, 1992 .

Almost-primes in arithmetic progressions and short intervals

D. R. Heath-Brown, 1978, Mathematical Proceedings of the Cambridge Philosophical Society.

Diophantine approximation with square-free numbers

D. R. Heath-Brown, 1984 .

Searching for Solutions of x 3 + y 3 + z 3 = k

D. R. Heath-Brown, 1992 .

Primes Represented by x 3 + 2 y 3

D. R. Heath-Brown, 2022 .

Irreducible polynomials over finite fields produced by composition of quadratics

Giacomo Micheli, D. R. Heath-Brown, 2019, Revista Matemática Iberoamericana.

Odd perfect numbers

D. R. Heath-Brown, 1994, Mathematical Proceedings of the Cambridge Philosophical Society.

Edmund Landau: Collected Works

D. R. Heath-Brown, 1989 .

The Solubility of Diagonal Cubic Diophantine Equations

D. R. Heath-Brown, 1999 .

The circle method and diagonal cubic forms

D. R. Heath-Brown, 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

Weyl's inequality and hua's inequality

D. R. Heath-Brown, 1989 .

Counting Rational Points on Cubic Surfaces

D. R. Heath-Brown, 2015 .

Square-full numbers in short intervals

D. R. Heath-Brown, 1991, Mathematical Proceedings of the Cambridge Philosophical Society.

The Fourth Power Moment of the Riemann Zeta Function

D. R. Heath-Brown, 1979 .

The first case of Fermat's last theorem

D. R. Heath-Brown, L. Adleman, 1985 .

Weyl's Inequality, Hua's Inequality, and Waring's Problem

D. R. Heath-Brown, 1988 .

Zeros of systems of 𝔭-adic quadratic forms

D. R. Heath-Brown, 2010, Compositio Mathematica.

Zeros of systems of ${\mathfrak p}$-adic Quadratic Forms

D. R. Heath-Brown, 2008, 0810.1122.

A pr 2 00 9 Zeros of Systems of p-adic Quadratic Forms

D. R. Heath-Brown, 2009 .

RANDOM MATRICES, FROBENIUS EIGENVALUES, AND MONODROMY (American Mathematical Society Colloquium Publications 45) By N ICHOLAS M. K ATZ and P ETER S ARNAK : 419 pp., US$69.00, ISBN 0 8218 1017 0 (American Mathematical Society, 1998).

D. R. Heath-Brown, 2000 .

DENSITY OF RATIONAL POINTS ON A QUADRIC BUNDLE IN P × P

D. R. Heath-Brown, 2019 .

The average analytic rank of elliptic curves

D. R. Heath-Brown, 2003, math/0305114.

Simple Zeros of the Riemann Zeta-Function on the Critical Line

D. R. Heath-Brown, 1979 .

QUADRATIC CLASS NUMBERS DIVISIBLE BY 3

D. R. Heath-Brown, 2007 .

Almost-prime k-tuples

D. R. Heath-Brown, 1997 .

Quadratic polynomials represented by norm forms

D. R. Heath-Brown, T. Browning, Tim D Browning, 2011, 1109.0232.

Lectures on sieves

D. R. Heath-Brown, 2002, math/0209360.

Cubic Forms in Ten Variables

D. R. Heath-Brown, 1983 .

The distribution of Kummer sums at prime arguments.

S. J. Patterson, D. R. Heath-Brown, S. Patterson, 1979 .

The density of rational points on Cayley's cubic surface

D. R. Heath-Brown, 2002, math/0210333.

(2017). Forms in many variables and differing degrees. Journal of the European Mathematical Society , 19 (2), 357-394.

D. R. Heath-Brown, 2015 .

Rational points on quartic hypersurfaces

D. R. Heath-Brown, T. Browning, 2007, math/0701348.

The density of rational points on non-singular hypersurfaces

D. R. Heath-Brown, T. Browning, J. Starr, 1994, math/0505186.

The density of rational points on the cubic surface X30= X1X2X3

D. R. Heath-Brown, B. Z. Moroz, 1999, Mathematical Proceedings of the Cambridge Philosophical Society.

The Distribution of Rational Points on Conics

D. R. Heath-Brown, 2022, 2203.13889.

Density of non‐residues in Burgess‐type intervals and applications

D. R. Heath-Brown, W. Banks, I. Shparlinski, 2006, math/0607692.

Heilbronn's exponential sum and transcendence theory

D. R. Heath-Brown, 2002 .

Counting Rational Points on Algebraic Varieties

D. R. Heath-Brown, T. Browning, P. Salberger, 2004, math/0410117.

Lagrange's four squares theorem with one prime and threealmost--prime variables

D. R. Heath-Brown, D. Tolev, 2003 .

The growth rate of the Dedekind Zeta-function on the critical line

D. R. Heath-Brown, 1988 .

The divisor function $d_3(n)$ in arithmetic progressions

D. R. Heath-Brown, 1986 .

The fractional part of αn k

D. R. Heath-Brown, 1988 .

Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial.

D. R. Heath-Brown, J. Conrey, 1985 .

Counting rational points on smooth cyclic covers

D. R. Heath-Brown, L. Pierce, 2011, 1109.1455.

Simultaneous Integer Values of Pairs of Quadratic Forms

D. R. Heath-Brown, L. Pierce, 2013, 1309.6767.

On the Representation of Primes by Cubic Polynomials in Two Variables

D. R. Heath-Brown, B. Z. Moroz, 2004 .

Sums and differences of three kth powers

D. R. Heath-Brown, 2008, 0806.4330.

Christopher Hooley. 7 August 1928—13 December 2018

D. R. Heath-Brown, 2020, BIOGRAPHICAL MEMOIRS OF FELLOWS OF THE ROYAL SOCIETY.

Integral points on cubic hypersurfaces

D. R. Heath-Brown, T. Browning, 2006, math/0611086.

Cubic forms in 10 variables

D. R. Heath-Brown, 1984 .

Powerfree Values of Polynomials

D. R. Heath-Brown, 2011, 1103.2028.

Plane curves in boxes and equal sums of two powers

D. R. Heath-Brown, T. Browning, 2005, math/0506497.

J an 2 01 2 p-adic Zeros of Systems of Quadratic Forms

D. R. Heath-Brown, 2013 .

Primes Represented by Binary Cubic Forms

D. R. Heath-Brown, D. R. Heath-Brown, B. Z. Moroz, 2002 .

The Pjateckiĭ-S̆apiro prime number theorem

D. R. Heath-Brown, 1983 .

Large gaps between consecutive prime numbers containing perfect powers

D. R. Heath-Brown, S. Konyagin, Kevin Ford, 2014, 1411.6543.

Prime number theory and the Riemann Zeta-function

D. R. Heath-Brown, 2005 .

Small solutions of quadratic congruences

D. R. Heath-Brown, 1985, Glasgow Mathematical Journal.

Zeros of pairs of quadratic forms

D. R. Heath-Brown, 2013, Journal für die Reine und Angewandte Mathematik.

The size of Selmer groups for the congruent number problem

D. R. Heath-Brown, 1993 .

Rational points on the intersection of three quadrics

D. R. Heath-Brown, 2015, 1510.01191.

Zeros of p‐adic forms

D. R. Heath-Brown, 2008, 0805.0534.

Artin's Conjecture on Zeros of p-adic Forms

D. R. Heath-Brown, 2010, 1002.3754.

RATIONAL POINTS ON INTERSECTIONS OF CUBIC AND QUADRIC HYPERSURFACES

D. R. Heath-Brown, T. Browning, R. Dietmann, 2013, Journal of the Institute of Mathematics of Jussieu.

Density of rational points on a quadric bundle in P 3 × P 3

D. R. Heath-Brown, T. Browning, 2018, 1805.10715.

A new form of the circle method, and its application to quadratic forms.

D. R. Heath-Brown, D.R. Heath-Brown, Magdalene College, 1996 .

The average rank of elliptic curves

D. R. Heath-Brown, 2004 .

A mean value estimate for real character sums

D. R. Heath-Brown, 1995 .

VAN DER CORPUT'S METHOD OF EXPONENTIAL SUMS (London Mathematical Society Lecture Note Series 126)

D. R. Heath-Brown, 1991 .

Prime values of $$a^2 + p^4$$a2+p4

D. R. Heath-Brown, Xiannan Li, 2017 .

Prime values of a2+p4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a^2 + p^4$$\end{document}

D. R. Heath-Brown, Xiannan Li, 2016, Inventiones mathematicae.

Primes values of $a^2 + p^4$

D. R. Heath-Brown, Xiannan Li, 2015, 1504.00531.

Rational Points and Analytic Number Theory

D. R. Heath-Brown, 2004 .

Exponential decay in the frequency of analytic ranks of automorphic L-functions

D. R. Heath-Brown, P. Michel, 2000 .

A note on the 2--part of Sha for the congruent number curves

D. R. Heath-Brown, 2007 .

The size of Selmer groups for the congruent number problem, II

D. R. Heath-Brown, 1994 .

Forms in many variables and differing degrees

D. R. Heath-Brown, T. Browning, Roger Heath-Brown, 2014, 1403.5937.

Counting rational points on quadric surfaces

D. R. Heath-Brown, T. Browning, 2018, Discrete Analysis.

Simultaneous equal sums of three powers

D. R. Heath-Brown, T. Browning, 2005, math/0509152.

The Density of Rational Points on Non‐Singular Hypersurfaces, I

D. R. Heath-Brown, T. Browning, Tim D Browning, 2005, math/0502243.

Counting rational points on hypersurfaces

D. R. Heath-Brown, T. Browning, 2004, math/0404456.

2 00 5 Counting Rational Points on Hypersurfaces

D. R. Heath-Brown, T. Browning, 2009 .

A pr 2 00 4 Counting Rational Points on Hypersurfaces

D. R. Heath-Brown, T. Browning, 2009 .

2 2 A pr 2 00 5 Counting Rational Points on Algebraic Varieties

D. R. Heath-Brown, T. Browning, P. Salberger, 2008 .

Cubic forms in 14 variables

D. R. Heath-Brown, 2007 .

A Multiple Exponential Sum to Modulus p 2

D. R. Heath-Brown, 1985, Canadian Mathematical Bulletin.

Equal sums of three powers

D. R. Heath-Brown, T. Browning, 2004 .

7 S ep 2 00 5 Simultaneous equal sums of three powers

D. R. Heath-Brown, T. Browning, 2022 .

The density of rational points on cubic surfaces

D. R. Heath-Brown, 1997 .

The largest prime factor of X3+2

D. R. Heath-Brown, 2001 .

Integers Represented as a Sum of Primes and Powers of Two

D. R. Heath-Brown, Jan-Christoph Puchta, 2002, math/0201299.

The cubic case of Vinogradov’s mean value theorem

D. R. Heath-Brown, 2015, Essential Number Theory.

Kummer’s conjecture for cubic Gauss sums

D. R. Heath-Brown, 2000 .

Searching for Salutions of x 3 + y3 + z3 = k

D. R. Heath-Brown, 1992 .

Pair correlation for fractional parts of αn2

D. R. Heath-Brown, 2009, Mathematical Proceedings of the Cambridge Philosophical Society.

Density of non-residues in short intervals

D. R. Heath-Brown, W. Banks, I. Shparlinski, 2006 .

Komaravolu Chandrasekharan (1920–2017)

D. R. Heath-Brown, 2018 .

Equidistribution for Solutions of $p+m^2+n^2=N$, and for Ch\^{a}telet Surfaces

D. R. Heath-Brown, 2022, 2212.12587.

Quadratic polynomials represented by norm forms

D. R. Heath-Brown, T. Browning, 2012, Geometric and Functional Analysis.

A note on the differences between consecutive primes

D. R. Heath-Brown, D. Goldston, 1984 .

Prime Numbers in Short Intervals and a Generalized Vaughan Identity

D. R. Heath-Brown, 1982, Canadian Journal of Mathematics - Journal Canadien de Mathematiques.

On simple zeros of the Riemann zeta‐function

D. R. Heath-Brown, H. Bui, 2013, 1302.5018.

Permutation groups, simple groups, and sieve methods

D. R. Heath-Brown, C. Praeger, A. Shalev, 2005 .

FRACTIONAL MOMENTS OF THE RIEMANN ZETA-FUNCTION, II

D. R. Heath-Brown, 1993 .

Fractional Moments of the Riemann Zeta‐Function

D. R. Heath-Brown, 1981 .

The first case of fermat’s last theorem

D. R. Heath-Brown, 1985 .

The Differences Between Consecutive Primes. V

D. R. Heath-Brown, 2019, 1906.09555.

O ct 2 00 4 Counting Rational Points on Algebraic Varieties

D. R. Heath-Brown, T. Browning, P. Salberger, 2004 .

The mean value theorem for the Riemann zeta-function

D. R. Heath-Brown, 1978 .

ON THE DISTRIBUTION OF GAPS BETWEEN ZEROS OF THE ZETA-FUNCTION

D. R. Heath-Brown, J. Conrey, Amit Ghosh, 1985 .

ANALYTIC METHODS FOR THE DISTRIBUTION OF RATIONAL POINTS ON ALGEBRAIC VARIETIES

D. R. Heath-Brown, 2007 .

The largest prime factor of the integers in an interval, II

D. R. Heath-Brown, C. Jia, 1998 .