## Heath-Brown, Roger

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 Author ID: heath-brown.roger Published as: Heath-Brown, D. R.; Heath-Brown, Roger; Heath-Brown, David Rodney; Heath-Brown, D. Roger; Heath-Brown, D. more...less Homepage: https://www.maths.ox.ac.uk/people/roger.heath-brown External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef
 Documents Indexed: 185 Publications since 1974 5 Contributions as Editor · 8 Further Contributions Reviewing Activity: 724 Reviews Biographic References: 1 Publication Co-Authors: 48 Co-Authors with 60 Joint Publications 1,601 Co-Co-Authors
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### Co-Authors

 128 single-authored 17 Browning, Timothy Daniel 6 Moroz, Boris Zelikovich Baruch ben Zelik 4 Pierce, Lillian B. 3 Iwaniec, Henryk 2 Banks, William David 2 Bui, Hung Manh 2 Conrey, John Brian 2 Dietmann, Rainer 2 Goldston, Daniel Alan 2 Jia, Chaohua 2 Konyagin, Sergeĭ Vladimirovich 2 Li, Xiannan 2 Manin, Yuriĭ Ivanovich 2 Shparlinski, Igor E. 1 Adleman, Leonard Max 1 Balasubramanian, Ramachandran 1 Colliot-Thélène, Jean-Louis 1 Davenport, Harold 1 Demeter, Ciprian 1 Dieulefait, Luis Victor 1 Evelyn, Cecil John Alvin 1 Faltings, Gerd 1 Ford, Kevin B. 1 Freeman, D. Eric 1 Friedlander, John Benjamin 1 Gallardo, Luis Henri 1 Garaev, Moubariz Z. 1 Ghosh, Amit 1 Gonek, Steven M. 1 Guth, Lawrence David 1 Halberstam, Heini 1 Hardy, Godfrey Harold 1 Huxley, Martin N. 1 Kaczorowski, Jerzy 1 Lioen, Walter M. 1 Macintyre, Angus John 1 Matiyasevich, Yuriĭ Vladimirovich 1 Michel, Philippe Gabriel 1 Micheli, Giacomo 1 Monsky, Paul 1 Patterson, Samuel James 1 Praeger, Cheryl Elisabeth 1 Richert, Hans-Egon 1 Salberger, Per 1 Schlage-Puchta, Jan-Christoph 1 Shalev, Aner 1 Silverman, Joseph Hillel 1 Skorobogatov, Alexei Nikolaïevitch 1 Starr, Jason Michael 1 te Riele, Herman 1 Testa, Damiano 1 Titchmarsh, Edward Charles 1 Tolev, Doychin I. 1 Tsang, Kai-Man 1 Vaughan, Robert C. 1 Wang, Hong 1 Wiles, Andrew John 1 Wilson, Pelham Mark Hedley 1 Wintenberger, Jean-Pierre 1 Wright, Edward Maitland
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### Serials

 14 Acta Arithmetica 12 Journal of the London Mathematical Society. Second Series 12 Proceedings of the London Mathematical Society. Third Series 11 Journal für die Reine und Angewandte Mathematik 8 Inventiones Mathematicae 8 Mathematika 7 Bulletin of the London Mathematical Society 6 Mathematical Proceedings of the Cambridge Philosophical Society 6 The Quarterly Journal of Mathematics. Oxford Second Series 5 Journal of Number Theory 4 Duke Mathematical Journal 3 Mathematische Annalen 3 Mathematische Zeitschrift 2 Israel Journal of Mathematics 2 Mathematics of Computation 2 Acta Mathematica 2 Canadian Journal of Mathematics 2 Compositio Mathematica 2 Functiones et Approximatio. Commentarii Mathematici 2 The Journal of the Indian Mathematical Society. New Series 2 Revista Matemática Iberoamericana 2 Forum Mathematicum 2 IMRN. International Mathematics Research Notices 2 Geometric and Functional Analysis. GAFA 2 Journal of Mathematical Sciences (New York) 2 The Quarterly Journal of Mathematics 2 Journal of the Institute of Mathematics of Jussieu 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Glasgow Mathematical Journal 1 Hardy-Ramanujan Journal 1 Analysis 1 Science in China. Series A 1 Bulletin of the American Mathematical Society. New Series 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Finite Fields and their Applications 1 The Asian Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 International Journal of Number Theory 1 Bonner Mathematische Schriften 1 Lecture Notes in Mathematics 1 London Mathematical Society Lecture Note Series 1 Proceedings of the Steklov Institute of Mathematics 1 Science China. Mathematics 1 Discrete Analysis 1 Cambridge Mathematical Library
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### Fields

 191 Number theory (11-XX) 29 Algebraic geometry (14-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 2 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX)

### Citations contained in zbMATH Open

166 Publications have been cited 2,312 times in 1,728 Documents Cited by Year
The theory of the Riemann zeta-function. 2nd ed., rev. by D. R. Heath-Brown. Zbl 0601.10026
Titchmarsh, E. C.
1986
An introduction to the theory of numbers. Edited and revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles. 6th ed. Zbl 1159.11001
Hardy, G. H.; Wright, E. M.
2008
The Pjateckii-Sapiro prime number theorem. Zbl 0513.10042
Heath-Brown, D. R.
1983
The fourth power moment of the Riemann zeta function. Zbl 0403.10018
Heath-Brown, D. R.
1979
Artin’s conjecture for primitive roots. Zbl 0586.10025
Heath-Brown, D. R.
1986
The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène). Zbl 1039.11044
Heath-Brown, D. R.
2002
Prime numbers in short intervals and a generalized Vaughan identity. Zbl 0478.10024
Heath-Brown, D. R.
1982
Zero-free regions for Dirichlet $$L$$-functions and the least prime in an arithmetic progression. Zbl 0739.11033
Heath-Brown, D. R.
1992
New bounds for Gauss sums derived from $$k$$th powers, and for Heilbronn’s exponential sum. Zbl 0983.11052
Heath-Brown, D. R.; Konyagin, S.
2000
A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049
Heath-Brown, D. R.
1996
The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Zbl 0815.11032
Heath-Brown, D. R.
1994
The twelfth power moment of the Riemann-function. Zbl 0394.10020
Heath-Brown, D. R.
1978
A mean value estimate for real character sums. Zbl 0828.11040
Heath-Brown, D. R.
1995
Lattice points in the sphere. Zbl 0929.11040
Heath-Brown, D. R.
1999
Integer sets containing no arithmetic progressions. Zbl 0589.10062
Heath-Brown, D. R.
1987
The distribution and moments of the error term in the Dirichlet divisor problems. Zbl 0725.11045
Heath-Brown, D. R.
1992
Fractional moments of the Riemann zeta-function. Zbl 0431.10024
Heath-Brown, D. R.
1981
The square sieve and consecutive square-free numbers. Zbl 0514.10038
Heath-Brown, D. R.
1984
Cubic forms in 10 variables. Zbl 0494.10012
Heath-Brown, D. R.
1983
Analytic methods for Diophantine equations and Diophantine inequalities. Edited and prepared by T. D. Browning. With a preface by R. C. Vaughan, D. R. Heath-Brown and D. E. Freeman. 2nd ed. Zbl 1125.11018
Davenport, Harold
2005
Hybrid bounds for Dirichlet L-functions. Zbl 0362.10035
Heath-Brown, D. R.
1978
Integers represented as a sum of primes and powers of two. Zbl 1097.11050
Heath-Brown, D. R.; Puchta, J.-C.
2002
The distribution of Kummer sums at prime arguments. Zbl 0412.10028
Heath-Brown, D. R.; Patterson, S. J.
1979
Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. Zbl 0549.10030
Balasubramanian, R.; Conrey, J. B.; Heath-Brown, D. R.
1985
The divisor function $$d_ 3(n)$$ in arithmetic progressions. Zbl 0549.10034
Heath-Brown, D. R.
1986
Hybrid bounds for Dirichlet L-functions. II. Zbl 0396.10030
Heath-Brown, D. R.
1980
Diophantine approximation with square-free numbers. Zbl 0539.10026
Heath-Brown, D. R.
1984
The number of primes in a short interval. Zbl 0646.10032
Heath-Brown, D. R.
1988
The size of Selmer groups for the congruent number problem. Zbl 0808.11041
Heath-Brown, D. R.
1993
Pair correlation for fractional parts of $$\alpha n^2$$. Zbl 1239.11081
Heath-Brown, D. R.
2010
Almost-primes in arithmetic progressions and short intervals. Zbl 0375.10027
Heath-Brown, D. R.
1978
Simple zeros of the Riemann zeta-function on the critical line. Zbl 0409.10027
Heath-Brown, D. R.
1979
On the difference between consecutive primes. Zbl 0424.10028
Heath-Brown, D. R.; Iwaniec, H.
1979
Cubic forms in 14 variables. Zbl 1135.11031
Heath-Brown, D. R.
2007
Primes represented by $$x^3+ 2y^3$$. Zbl 1007.11055
Heath-Brown, D. R.
2001
The average analytic rank of elliptic curves. Zbl 1063.11013
Heath-Brown, D. R.
2004
Counting rational points on algebraic varieties. Zbl 1098.14013
Browning, T. D.; Heath-Brown, D. R.; Salberger, P.
2006
The density of rational points on cubic surfaces. Zbl 0863.11021
Heath-Brown, D. R.
1997
The growth rate of the Dedekind zeta-function on the critical line. Zbl 0583.12011
Heath-Brown, D. R.
1988
Prime twins and Siegel zeros. Zbl 0517.10044
Heath-Brown, D. R.
1983
Gaps between primes, and the pair correlation of zeros of the zeta-function. Zbl 0414.10044
Heath-Brown, D. R.
1982
Weyl’s inequality, Hua’s inequality and Waring’s problem. Zbl 0619.10046
Heath-Brown, D. R.
1988
The divisor function at consecutive integers. Zbl 0529.10040
Heath-Brown, D. R.
1984
A new $$k$$th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110
Heath-Brown, D. R.
2017
Sign changes of $$E(T)$$, $$\Delta(x)$$, and $$P(x)$$. Zbl 0810.11046
Heath-Brown, D. R.; Tsang, K.-M.
1994
Counting rational points on hypersurfaces. Zbl 1079.11033
Browning, T. D.; Heath-Brown, D. R.
2005
An estimate for Heilbronn’s exponential sum. Zbl 0857.11041
Heath-Brown, D. R.
1996
The distribution of $$\alpha p$$ modulo one. Zbl 1023.11034
Heath-Brown, D. R.; Jia, Chaohua
2002
The fourth power mean of Dirichlet’s L-functions. Zbl 0479.10027
Heath-Brown, D. R.
1981
Forms in many variables and differing degrees. Zbl 1383.11039
Browning, Tim; Heath-Brown, Roger
2017
Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006
Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E.
2008
Counting rational points on algebraic varieties. Zbl 1152.11027
Heath-Brown, D. R.
2006
Rational solutions of certain equations involving norms. Zbl 1023.11033
Heath-Brown, Roger; Skorobogatov, Alexei
2002
Small solutions of quadratic congruences. Zbl 0581.10008
Heath-Brown, D. R.
1985
Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050
Heath-Brown, D. R.; Tolev, D. I.
2003
An asymptotic series for the mean value of Dirichlet $$L$$-functions. Zbl 0457.10020
Heath-Brown, D. R.
1981
The least square-free number in an arithmetic progression. Zbl 0493.10045
Heath-Brown, D. R.
1982
On the density of the zeros of the Dedekind zeta-function. Zbl 0325.12003
Heath-Brown, D. R.
1977
On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050
Heath-Brown, D. R.; Moroz, B. Z.
2004
Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042
Heath-Brown, D. R.
2000
Odd perfect numbers. Zbl 0805.11005
Heath-Brown, D. R.
1994
On the distribution of gaps between zeros of the zeta-function. Zbl 0557.10028
Conrey, J. B.; Ghosh, A.; Goldston, D.; Gonek, S. M.; Heath-Brown, D. R.
1985
The first case of Fermat’s last theorem. Zbl 0557.10034
Adleman, L. M.; Heath-Brown, D. R.
1985
On simple zeros of the Riemann zeta-function. Zbl 1291.11118
Bui, H. M.; Heath-Brown, D. R.
2013
Almost-prime $$k$$-tuples. Zbl 0886.11052
Heath-Brown, D. R.
1997
Burgess’s bounds for character sums. Zbl 1328.11088
Heath-Brown, D. R.
2013
Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031
Heath-Brown, D. R.
1993
Primes represented by binary cubic forms. Zbl 1030.11046
Heath-Brown, D. R.; Moroz, B. Z.
2002
The largest prime factor of $$X^3+2$$. Zbl 1023.11048
Heath-Brown, D. R.
2001
On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055
Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E.
2005
Siegel zeros and the least prime in an arithmetic progression. Zbl 0715.11049
Heath-Brown, D. R.
1990
Three primes and an almost-prime in arithmetic progression. Zbl 0425.10051
Heath-Brown, D. R.
1981
Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150
Heath-Brown, D. R.
2008
The mean value theorem for the Riemann zeta-function. Zbl 0387.10023
Heath-Brown, D. R.
1979
The differences between consecutive primes. Zbl 0387.10025
Heath-Brown, D. R.
1978
Zero density estimates for the Riemann zeta-function and Dirichlet L-functions. Zbl 0393.10043
Heath-Brown, D. R.
1979
Rational points on quartic hypersurfaces. Zbl 1169.11027
Browning, T. D.; Heath-Brown, D. R.
2009
Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 1498.11233
Heath-Brown, David Rodney; Micheli, Giacomo
2019
The circle method and diagonal cubic forms. Zbl 0899.11051
Heath-Brown, D. R.
1998
The density of rational points on Cayley’s cubic surface. Zbl 1060.11038
Heath-Brown, D. R.
2003
A note on the differences between consecutive primes. Zbl 0514.10031
Heath-Brown, D. R.; Goldston, D. A.
1984
Zeros of $$p$$-adic forms. Zbl 1233.11039
Heath-Brown, D. R.
2010
Zeros of systems of $$\mathfrak p$$-adic quadratic forms. Zbl 1194.11047
Heath-Brown, D. R.
2010
Square-free values of $$n^2+1$$. Zbl 1312.11077
Heath-Brown, D. R.
2012
Burgess bounds for short mixed character sums. Zbl 1317.11083
Heath-Brown, D. R.; Pierce, L. B.
2015
The differences between consecutive primes. II. Zbl 0394.10021
Heath-Brown, D. R.
1979
The density of rational points on non-singular hypersurfaces. II. (With an appendix by J. M. Starr). Zbl 1104.11015
Browning, T. D.; Heath-Brown, D. R.; Starr, J. M.
2006
The density of zeros of forms for which weak approximation fails. Zbl 0778.11017
Heath-Brown, D. R.
1992
The density of rational points on non-singular hypersurfaces. Zbl 0808.11042
Heath-Brown, D. R.
1994
Almost-primes in short intervals. Zbl 0461.10041
Halberstam, H.; Heath-Brown, D. R.; Richert, H.-E.
1981
Arithmetic applications of Kloosterman sums. Zbl 1173.11339
Heath-Brown, D. R.
2000
Quadratic polynomials represented by norm forms. Zbl 1264.14032
Browning, T. D.; Heath-Brown, D. R.
2012
Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121
Heath-Brown, D. R.; Pierce, L. B.
2017
Prime values of $$a^2 + p^4$$. Zbl 1405.11124
Heath-Brown, D. R.; Li, Xiannan
2017
The ternary Goldbach problem. Zbl 0599.10041
Heath-Brown, D. R.
1985
The differences between consecutive primes. III. Zbl 0407.10032
Heath-Brown, D. R.
1979
Rational points on intersections of cubic and quadric hypersurfaces. Zbl 1327.11043
Browning, T. D.; Dietmann, R.; Heath-Brown, D. R.
2015
Power-free values of polynomials. Zbl 1287.11114
Heath-Brown, D. R.
2013
A note on the Chevalley-Warning theorems. Zbl 1247.11089
Heath-Brown, D. R.
2011
Integral points on cubic hypersurfaces. Zbl 1244.11066
Browning, T. D.; Heath-Brown, D. R.
2009
The geometric sieve for quadrics. Zbl 1481.11035
Browning, Tim D.; Heath-Brown, Roger
2021
Small cap decouplings. With an appendix by D. R. Heath-Brown. Zbl 1454.42008
Demeter, Ciprian; Guth, Larry; Wang, Hong
2020
Density of rational points on a quadric bundle in $$\mathbb{P}^3 \times \mathbb{P}^3$$. Zbl 1477.11058
Browning, T. D.; Heath-Brown, D. R.
2020
Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 1498.11233
Heath-Brown, David Rodney; Micheli, Giacomo
2019
Counting rational points on quadric surfaces. Zbl 1444.11142
Browning, T. D.; Heath-Brown, D. R.
2018
The differences between consecutive smooth numbers. Zbl 1446.11173
Heath-Brown, D. R.
2018
A new $$k$$th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110
Heath-Brown, D. R.
2017
Forms in many variables and differing degrees. Zbl 1383.11039
Browning, Tim; Heath-Brown, Roger
2017
Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121
Heath-Brown, D. R.; Pierce, L. B.
2017
Prime values of $$a^2 + p^4$$. Zbl 1405.11124
Heath-Brown, D. R.; Li, Xiannan
2017
Averages and moments associated to class numbers of imaginary quadratic fields. Zbl 1391.11151
Heath-Brown, D. R.; Pierce, L. B.
2017
Iteration of quadratic polynomials over finite fields. Zbl 1428.11204
Heath-Brown, D. R.
2017
Small solutions of quadratic congruences, and character sums with binary quadratic forms. Zbl 1375.11036
Heath-Brown, D. R.
2016
Almost prime triples and Chen’s theorem. Zbl 1390.11109
Heath-Brown, Roger; Li, Xiannan
2016
Burgess bounds for short mixed character sums. Zbl 1317.11083
Heath-Brown, D. R.; Pierce, L. B.
2015
Rational points on intersections of cubic and quadric hypersurfaces. Zbl 1327.11043
Browning, T. D.; Dietmann, R.; Heath-Brown, D. R.
2015
Large gaps between consecutive prime numbers containing perfect powers. Zbl 1391.11125
Ford, Kevin; Heath-Brown, D. R.; Konyagin, Sergei
2015
On simple zeros of the Riemann zeta-function. Zbl 1291.11118
Bui, H. M.; Heath-Brown, D. R.
2013
Burgess’s bounds for character sums. Zbl 1328.11088
Heath-Brown, D. R.
2013
Power-free values of polynomials. Zbl 1287.11114
Heath-Brown, D. R.
2013
$$p$$-adic zeros of systems of quadratic forms. Zbl 1333.11036
Heath-Brown, D. R.
2013
Square-free values of $$n^2+1$$. Zbl 1312.11077
Heath-Brown, D. R.
2012
Quadratic polynomials represented by norm forms. Zbl 1264.14032
Browning, T. D.; Heath-Brown, D. R.
2012
Counting rational points on smooth cyclic covers. Zbl 1248.14027
Heath-Brown, D. R.; Pierce, Lillian B.
2012
A note on the Chevalley-Warning theorems. Zbl 1247.11089
Heath-Brown, D. R.
2011
Pair correlation for fractional parts of $$\alpha n^2$$. Zbl 1239.11081
Heath-Brown, D. R.
2010
Zeros of $$p$$-adic forms. Zbl 1233.11039
Heath-Brown, D. R.
2010
Zeros of systems of $$\mathfrak p$$-adic quadratic forms. Zbl 1194.11047
Heath-Brown, D. R.
2010
A note on the fourth moment of Dirichlet $$L$$-functions. Zbl 1203.11056
Bui, H. M.; Heath-Brown, D. R.
2010
Fractional moments of Dirichlet $$L$$-functions. Zbl 1248.11059
Heath-Brown, D. R.
2010
Bounds for the cubic Weyl sum. Zbl 1282.11102
Heath-Brown, D. R.
2010
Counting rational points on cubic curves. Zbl 1229.11052
Heath-Brown, Roger; Testa, Damiano
2010
Rational points on quartic hypersurfaces. Zbl 1169.11027
Browning, T. D.; Heath-Brown, D. R.
2009
Integral points on cubic hypersurfaces. Zbl 1244.11066
Browning, T. D.; Heath-Brown, D. R.
2009
Convexity bounds for $$L$$-functions. Zbl 1169.11038
Heath-Brown, D. R.
2009
Sums and differences of three $$k$$th powers. Zbl 1182.11017
Heath-Brown, D. R.
2009
An introduction to the theory of numbers. Edited and revised by D. R. Heath-Brown and J. H. Silverman. With a foreword by Andrew Wiles. 6th ed. Zbl 1159.11001
Hardy, G. H.; Wright, E. M.
2008
Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006
Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E.
2008
Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150
Heath-Brown, D. R.
2008
Cubic forms in 14 variables. Zbl 1135.11031
Heath-Brown, D. R.
2007
Quadratic class numbers divisible by 3. Zbl 1140.11050
Heath-Brown, D. Roger
2007
Every sum of cubes in $$\mathbb F_2[t]$$ is a strict sum of 6 cubes. Zbl 1172.11045
Gallardo, Luis H.; Heath-Brown, D. R.
2007
Carmichael numbers with three prime factors. Zbl 1151.11047
Heath-Brown, D. R.
2007
Analytic methods for the distribution of rational points of algebraic varieties. Zbl 1181.11042
Heath-Brown, D. R.
2007
Counting rational points on algebraic varieties. Zbl 1098.14013
Browning, T. D.; Heath-Brown, D. R.; Salberger, P.
2006
Counting rational points on algebraic varieties. Zbl 1152.11027
Heath-Brown, D. R.
2006
The density of rational points on non-singular hypersurfaces. II. (With an appendix by J. M. Starr). Zbl 1104.11015
Browning, T. D.; Heath-Brown, D. R.; Starr, J. M.
2006
The density of rational points on non-singular hypersurfaces. I. Zbl 1174.11051
Browning, T. D.; Heath-Brown, D. R.
2006
Analytic methods for Diophantine equations and Diophantine inequalities. Edited and prepared by T. D. Browning. With a preface by R. C. Vaughan, D. R. Heath-Brown and D. E. Freeman. 2nd ed. Zbl 1125.11018
Davenport, Harold
2005
Counting rational points on hypersurfaces. Zbl 1079.11033
Browning, T. D.; Heath-Brown, D. R.
2005
On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055
Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E.
2005
Plane curves in boxes and equal sums of two powers. Zbl 1174.11380
Browning, T. D.; Heath-Brown, D. R.
2005
Permutation groups, simple groups, and sieve methods. Zbl 1091.11035
Heath-Brown, D. R.; Praeger, Cheryl E.; Shalev, Aner
2005
Prime number theory and the Riemann zeta-function. Zbl 1204.11144
Heath-Brown, D. R.
2005
The average analytic rank of elliptic curves. Zbl 1063.11013
Heath-Brown, D. R.
2004
On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050
Heath-Brown, D. R.; Moroz, B. Z.
2004
Equal sums of three powers. Zbl 1135.11052
Browning, T. D.; Heath-Brown, D. R.
2004
Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050
Heath-Brown, D. R.; Tolev, D. I.
2003
The density of rational points on Cayley’s cubic surface. Zbl 1060.11038
Heath-Brown, D. R.
2003
Linear relations amongst sums of two squares. Zbl 1161.11387
Heath-Brown, D. R.
2003
Proceedings of the session in analytic number theory and Diophantine equations held in Bonn, Germany, January–June, 2002. Zbl 1050.11003
2003
Lectures on sieves. Zbl 1070.11045
Heath-Brown, D. R.
2003
The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène). Zbl 1039.11044
Heath-Brown, D. R.
2002
Integers represented as a sum of primes and powers of two. Zbl 1097.11050
Heath-Brown, D. R.; Puchta, J.-C.
2002
The distribution of $$\alpha p$$ modulo one. Zbl 1023.11034
Heath-Brown, D. R.; Jia, Chaohua
2002
Rational solutions of certain equations involving norms. Zbl 1023.11033
Heath-Brown, Roger; Skorobogatov, Alexei
2002
Primes represented by binary cubic forms. Zbl 1030.11046
Heath-Brown, D. R.; Moroz, B. Z.
2002
Heilbronn’s exponential sum and transcendence theory. Zbl 1177.11072
Heath-Brown, D. R.
2002
Primes represented by $$x^3+ 2y^3$$. Zbl 1007.11055
Heath-Brown, D. R.
2001
The largest prime factor of $$X^3+2$$. Zbl 1023.11048
Heath-Brown, D. R.
2001
New bounds for Gauss sums derived from $$k$$th powers, and for Heilbronn’s exponential sum. Zbl 0983.11052
Heath-Brown, D. R.; Konyagin, S.
2000
Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042
Heath-Brown, D. R.
2000
Arithmetic applications of Kloosterman sums. Zbl 1173.11339
Heath-Brown, D. R.
2000
Exponential decay in the frequency of analytic ranks of automorphic $$L$$-functions. Zbl 1166.11326
Heath-Brown, D. R.; Michel, P.
2000
Lattice points in the sphere. Zbl 0929.11040
Heath-Brown, D. R.
1999
The density of rational points on the cubic surface $$X_0^3=X_1X_2X_3$$. Zbl 0938.11016
Heath-Brown, D. R.; Moroz, B. Z.
1999
The solubility of diagonal cubic Diophantine equations. Zbl 1029.11010
Heath-Brown, D. R.
1999
A note on the paper ‘consecutive almost-primes’. Zbl 1141.11318
Heath-Brown, D. R.
1999
The circle method and diagonal cubic forms. Zbl 0899.11051
Heath-Brown, D. R.
1998
The largest prime factor of the integers in an interval. II. Zbl 1066.11506
Heath-Brown, D. R.; Jia, Chaohua
1998
Counting rational points on cubic surfaces. Zbl 0926.11046
Heath-Brown, Roger
1998
The density of rational points on cubic surfaces. Zbl 0863.11021
Heath-Brown, D. R.
1997
Almost-prime $$k$$-tuples. Zbl 0886.11052
Heath-Brown, D. R.
1997
A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049
Heath-Brown, D. R.
1996
An estimate for Heilbronn’s exponential sum. Zbl 0857.11041
Heath-Brown, D. R.
1996
The largest prime factor of the integers in an interval. Zbl 0867.11064
Heath-Brown, D. R.
1996
A mean value estimate for real character sums. Zbl 0828.11040
Heath-Brown, D. R.
1995
The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Zbl 0815.11032
Heath-Brown, D. R.
1994
Sign changes of $$E(T)$$, $$\Delta(x)$$, and $$P(x)$$. Zbl 0810.11046
Heath-Brown, D. R.; Tsang, K.-M.
1994
Odd perfect numbers. Zbl 0805.11005
Heath-Brown, D. R.
1994
The density of rational points on non-singular hypersurfaces. Zbl 0808.11042
Heath-Brown, D. R.
1994
The size of Selmer groups for the congruent number problem. Zbl 0808.11041
Heath-Brown, D. R.
1993
Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031
Heath-Brown, D. R.
1993
On solving the diophantine equation $$x^ 3+y^ 3+z^ 3=k$$ on a vector computer. Zbl 0783.11046
Heath-Brown, D. R.; Lioen, W. M.; te Riele, Herman J. J.
1993
The Dirichlet divisor problem. Zbl 0791.11048
Heath-Brown, D. R.
1993
Zero-free regions for Dirichlet $$L$$-functions and the least prime in an arithmetic progression. Zbl 0739.11033
Heath-Brown, D. R.
1992
The distribution and moments of the error term in the Dirichlet divisor problems. Zbl 0725.11045
Heath-Brown, D. R.
1992
The density of zeros of forms for which weak approximation fails. Zbl 0778.11017
Heath-Brown, D. R.
1992
Calabi-Yau threefolds with $$\rho > 13$$. Zbl 0759.14030
Heath-Brown, D. R.; Wilson, P. M. H.
1992
Zero-free regions of $$\zeta (s)$$ and $$L(s,\chi)$$. Zbl 0791.11042
Heath-Brown, D. R.
1992
...and 66 more Documents
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### Cited by 1,350 Authors

 59 Shparlinski, Igor E. 38 Browning, Timothy Daniel 35 Heath-Brown, Roger 27 Zhai, Wenguang 21 Wooley, Trevor D. 20 Ivić, Aleksandar 20 Lu, Guangshi 18 Harman, Glyn 17 Iwaniec, Henryk 15 Baier, Stephan 15 Michel, Philippe Gabriel 15 Zaharescu, Alexandru 14 Blomer, Valentin 14 Fouvry, Etienne 14 Goldston, Daniel Alan 13 Baker, Roger C. 13 Brüdern, Jörg 13 Li, Jinjiang 12 Banks, William David 12 Bourgain, Jean 12 Cao, Xiaodong 12 de la Bretèche, Régis 12 Murty, Maruti Ram 12 Tsang, Kai-Man 12 Zhang, Min 11 Kowalski, Emmanuel 11 Laurinčikas, Antanas 11 Pintz, Janos 11 Soundararajan, Kannan 11 Tao, Terence 11 Zhao, Liangyi 10 Cai, Yingchun 10 Cochrane, Todd 10 Friedlander, John Benjamin 10 Hu, Liqun 10 Liu, Zhixin 10 Munshi, Ritabrata 10 Perelli, Alberto 10 Pierce, Lillian B. 10 Tanigawa, Yoshio 10 Young, Matthew P. 9 Bazzanella, Danilo 9 Conrey, John Brian 9 Dietmann, Rainer 9 Garaev, Moubariz Z. 9 Liu, Huafeng 9 Radziwiłł, Maksym 8 Brandes, Julia 8 Chamizo Lorente, Fernando 8 Chang, Mei-Chu 8 Fomenko, Oleg Mstislavovich 8 Gao, Peng 8 Konyagin, Sergeĭ Vladimirovich 8 Lau, Yuk-Kam 8 Pollack, Paul 8 Sankaranarayanan, Ayyadurai 8 Shkredov, Il’ya Dmitrievich 8 Steuding, Jörn 8 Vaughan, Robert C. 7 Derenthal, Ulrich 7 Dimitrov, Stoyan Ivanov 7 Ford, Kevin B. 7 Keating, Jonathan Peter 7 Korolëv, Maksim Aleksandrovich 7 Kumchev, Angel V. 7 Luca, Florian 7 Maynard, James 7 Nowak, Werner Georg 7 Robles, Nicolas 7 Salberger, Per 7 Sarnak, Peter Clive 7 Wu, Jie 7 Xiao, Stanley Yao 7 Yamagishi, Shuntaro 7 Zhao, Lilu 6 Aistleitner, Christoph 6 Gritsenko, Sergeĭ Aleksandrovich 6 Helfgott, Harald Andrés 6 Jutila, Matti Ilmari 6 Lamzouri, Youness 6 Milinovich, Micah B. 6 Motohashi, Yoichi 6 Munsch, Marc 6 Parsell, Scott T. 6 Rassias, Michael Th. 6 Rivat, Joël 6 Rubin, Karl Cooper 6 Rudnick, Zeév 6 Sawin, William F. 6 Schindler, Damaris 6 Sofos, Efthymios 6 Sono, Keiju 6 Sun, Haiwei 6 Tolev, Doychin I. 6 Xi, Ping 6 Zaman, Asif 6 Zhang, Deyu 5 Bettin, Sandro 5 Bui, Hung Manh 5 Chen, Yonggao ...and 1,250 more Authors
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### Cited in 222 Serials

 198 Journal of Number Theory 71 Mathematika 60 International Journal of Number Theory 45 Acta Arithmetica 39 Journal de Théorie des Nombres de Bordeaux 37 Mathematics of Computation 37 Mathematische Zeitschrift 37 Monatshefte für Mathematik 37 Proceedings of the American Mathematical Society 37 Transactions of the American Mathematical Society 36 Duke Mathematical Journal 32 Mathematische Annalen 32 The Ramanujan Journal 31 Functiones et Approximatio. Commentarii Mathematici 28 Advances in Mathematics 26 Acta Mathematica Hungarica 24 Lithuanian Mathematical Journal 24 Mathematical Proceedings of the Cambridge Philosophical Society 24 Inventiones Mathematicae 23 Journal für die Reine und Angewandte Mathematik 23 Algebra & Number Theory 23 Research in Number Theory 21 Rocky Mountain Journal of Mathematics 19 Compositio Mathematica 18 Israel Journal of Mathematics 18 Annals of Mathematics. Second Series 17 Mathematical Notes 16 Bulletin of the Australian Mathematical Society 16 Archiv der Mathematik 16 Bulletin of the American Mathematical Society. New Series 15 Journal of Mathematical Analysis and Applications 14 Forum Mathematicum 14 Finite Fields and their Applications 13 Acta Mathematica Sinica. New Series 12 Michigan Mathematical Journal 12 Indagationes Mathematicae. New Series 12 Journal of Mathematical Sciences (New York) 12 Science China. Mathematics 11 Journal d’Analyse Mathématique 11 Geometric and Functional Analysis. GAFA 11 Journal of the European Mathematical Society (JEMS) 10 Proceedings of the London Mathematical Society. Third Series 10 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 10 Proceedings of the Steklov Institute of Mathematics 9 Discrete Mathematics 9 Proceedings of the Japan Academy. Series A 9 Journal of the American Mathematical Society 9 Chebyshevskiĭ Sbornik 9 Forum of Mathematics, Sigma 8 Annales de l’Institut Fourier 8 Bulletin of the London Mathematical Society 8 Glasgow Mathematical Journal 8 Manuscripta Mathematica 8 Integers 8 Central European Journal of Mathematics 7 Periodica Mathematica Hungarica 7 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 7 Journal of the London Mathematical Society. Second Series 7 Revista Matemática Iberoamericana 7 Journal of the Australian Mathematical Society 7 Frontiers of Mathematics in China 7 Discrete Analysis 6 Communications in Mathematical Physics 6 Experimental Mathematics 6 Acta Mathematica Sinica. English Series 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 The Mathematical Intelligencer 5 Acta Mathematica 5 Journal of Soviet Mathematics 5 Designs, Codes and Cryptography 5 Expositiones Mathematicae 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 5 Forum of Mathematics, Pi 4 American Mathematical Monthly 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Canadian Journal of Mathematics 4 Journal of Algebra 4 Journal of Combinatorial Theory. Series A 4 Journal of Functional Analysis 4 Theoretical Computer Science 4 Combinatorica 4 Chinese Annals of Mathematics. Series B 4 Journal of Complexity 4 Journal of the Ramanujan Mathematical Society 4 Science in China. Series A 4 Sbornik: Mathematics 4 Taiwanese Journal of Mathematics 4 Portugaliae Mathematica. Nova Série 4 Research in the Mathematical Sciences 3 Mathematische Semesterberichte 3 Arkiv för Matematik 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Applied Mathematics and Computation 3 Commentarii Mathematici Helvetici 3 Czechoslovak Mathematical Journal 3 Pacific Journal of Mathematics 3 Rendiconti del Seminario Matematico della Università di Padova 3 St. Petersburg Mathematical Journal 3 Selecta Mathematica. New Series 3 Journal of High Energy Physics ...and 122 more Serials
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### Cited in 47 Fields

 1,623 Number theory (11-XX) 188 Algebraic geometry (14-XX) 50 Combinatorics (05-XX) 31 Dynamical systems and ergodic theory (37-XX) 28 Group theory and generalizations (20-XX) 25 Information and communication theory, circuits (94-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 24 Probability theory and stochastic processes (60-XX) 19 Partial differential equations (35-XX) 18 Convex and discrete geometry (52-XX) 17 Computer science (68-XX) 15 Field theory and polynomials (12-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Global analysis, analysis on manifolds (58-XX) 11 Topological groups, Lie groups (22-XX) 11 Quantum theory (81-XX) 10 History and biography (01-XX) 10 Functions of a complex variable (30-XX) 9 Several complex variables and analytic spaces (32-XX) 9 Numerical analysis (65-XX) 8 Special functions (33-XX) 7 Mathematical logic and foundations (03-XX) 7 Measure and integration (28-XX) 7 Approximations and expansions (41-XX) 6 Geometry (51-XX) 5 Commutative algebra (13-XX) 5 Associative rings and algebras (16-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 General and overarching topics; collections (00-XX) 4 Abstract harmonic analysis (43-XX) 4 Differential geometry (53-XX) 3 Real functions (26-XX) 3 Statistics (62-XX) 2 $$K$$-theory (19-XX) 2 Potential theory (31-XX) 2 Ordinary differential equations (34-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Fluid mechanics (76-XX) 2 Operations research, mathematical programming (90-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Nonassociative rings and algebras (17-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX)

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