Edit Profile (opens in new tab) Heath-Brown, Roger Co-Author Distance 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: 196 Publications since 1974, including 6 Additional arXiv Preprints 5 Contributions as Editor · 8 Further Contributions Reviewing Activity: 735 Reviews Biographic References: 1 Publication Co-Authors: 49 Co-Authors with 63 Joint Publications 1,819 Co-Co-Authors all top 5 Co-Authors 137 single-authored 18 Browning, Timothy Daniel 6 Moroz, Boris Zelikovich 4 Pierce, Lillian B. 3 Iwaniec, Henryk 2 Banks, William David 2 Bui, Hung Manh 2 Colliot-Thélène, Jean-Louis 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 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 all top 5 Serials 16 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 Journal of Number Theory 6 The Quarterly Journal of Mathematics. Oxford Second Series 4 Duke Mathematical Journal 3 Mathematische Annalen 3 Mathematische Zeitschrift 2 Israel Journal of Mathematics 2 Russian Mathematical Surveys 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 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 1 Essential Number Theory all top 5 Fields 200 Number theory (11-XX) 32 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 174 Publications have been cited 3,039 times in 2,220 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. 1,250 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. 477 2008 The Pjateckii-Sapiro prime number theorem. Zbl 0513.10042 Heath-Brown, D. R. 104 1983 The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène). Zbl 1039.11044 Heath-Brown, D. R. 96 2002 Artin’s conjecture for primitive roots. Zbl 0586.10025 Heath-Brown, D. R. 93 1986 The fourth power moment of the Riemann zeta function. Zbl 0403.10018 Heath-Brown, D. R. 92 1979 Prime numbers in short intervals and a generalized Vaughan identity. Zbl 0478.10024 Heath-Brown, D. R. 88 1982 A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049 Heath-Brown, D. R. 86 1996 A mean value estimate for real character sums. Zbl 0828.11040 Heath-Brown, D. R. 83 1995 Zero-free regions for Dirichlet \(L\)-functions and the least prime in an arithmetic progression. Zbl 0739.11033 Heath-Brown, D. R. 78 1992 The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Zbl 0815.11032 Heath-Brown, D. R. 77 1994 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 75 2005 The twelfth power moment of the Riemann-function. Zbl 0394.10020 Heath-Brown, D. R. 69 1978 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. 67 2000 Lattice points in the sphere. Zbl 0929.11040 Heath-Brown, D. R. 62 1999 Integer sets containing no arithmetic progressions. Zbl 0589.10062 Heath-Brown, D. R. 56 1987 Fractional moments of the Riemann zeta-function. Zbl 0431.10024 Heath-Brown, D. R. 54 1981 The distribution and moments of the error term in the Dirichlet divisor problems. Zbl 0725.11045 Heath-Brown, D. R. 53 1992 The square sieve and consecutive square-free numbers. Zbl 0514.10038 Heath-Brown, D. R. 49 1984 Hybrid bounds for Dirichlet L-functions. Zbl 0362.10035 Heath-Brown, D. R. 45 1978 Cubic forms in 10 variables. Zbl 0494.10012 Heath-Brown, D. R. 44 1983 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. 41 1985 The number of primes in a short interval. Zbl 0646.10032 Heath-Brown, D. R. 41 1988 Integers represented as a sum of primes and powers of two. Zbl 1097.11050 Heath-Brown, D. R.; Puchta, J.-C. 41 2002 The divisor function \(d_3(n)\) in arithmetic progressions. Zbl 0549.10034 Heath-Brown, D. R. 37 1986 Primes represented by \(x^3+ 2y^3\). Zbl 1007.11055 Heath-Brown, D. R. 37 2001 The size of Selmer groups for the congruent number problem. Zbl 0808.11041 Heath-Brown, D. R. 37 1993 The distribution of Kummer sums at prime arguments. Zbl 0412.10028 Heath-Brown, D. R.; Patterson, S. J. 37 1979 Hybrid bounds for Dirichlet L-functions. II. Zbl 0396.10030 Heath-Brown, D. R. 34 1980 Pair correlation for fractional parts of \(\alpha n^2\). Zbl 1239.11081 Heath-Brown, D. R. 32 2010 Diophantine approximation with square-free numbers. Zbl 0539.10026 Heath-Brown, D. R. 32 1984 The growth rate of the Dedekind zeta-function on the critical line. Zbl 0583.12011 Heath-Brown, D. R. 32 1988 Almost-primes in arithmetic progressions and short intervals. Zbl 0375.10027 Heath-Brown, D. R. 32 1978 A new \(k\)th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110 Heath-Brown, D. R. 32 2017 The average analytic rank of elliptic curves. Zbl 1063.11013 Heath-Brown, D. R. 31 2004 Counting rational points on algebraic varieties. Zbl 1098.14013 Browning, T. D.; Heath-Brown, D. R.; Salberger, P. 28 2006 Cubic forms in 14 variables. Zbl 1135.11031 Heath-Brown, D. R. 28 2007 The fourth power mean of Dirichlet’s L-functions. Zbl 0479.10027 Heath-Brown, D. R. 26 1981 Prime twins and Siegel zeros. Zbl 0517.10044 Heath-Brown, D. R. 26 1983 The density of rational points on cubic surfaces. Zbl 0863.11021 Heath-Brown, D. R. 25 1997 On the difference between consecutive primes. Zbl 0424.10028 Heath-Brown, D. R.; Iwaniec, H. 25 1979 Simple zeros of the Riemann zeta-function on the critical line. Zbl 0409.10027 Heath-Brown, D. R. 24 1979 Weyl’s inequality, Hua’s inequality and Waring’s problem. Zbl 0619.10046 Heath-Brown, D. R. 23 1988 Sign changes of \(E(T)\), \(\Delta(x)\), and \(P(x)\). Zbl 0810.11046 Heath-Brown, D. R.; Tsang, K.-M. 23 1994 Gaps between primes, and the pair correlation of zeros of the zeta-function. Zbl 0414.10044 Heath-Brown, D. R. 23 1982 Forms in many variables and differing degrees. Zbl 1383.11039 Browning, Tim; Heath-Brown, Roger 23 2017 The divisor function at consecutive integers. Zbl 0529.10040 Heath-Brown, D. R. 22 1984 The distribution of \(\alpha p\) modulo one. Zbl 1023.11034 Heath-Brown, D. R.; Jia, Chaohua 21 2002 Counting rational points on hypersurfaces. Zbl 1079.11033 Browning, T. D.; Heath-Brown, D. R. 21 2005 Counting rational points on algebraic varieties. Zbl 1152.11027 Heath-Brown, D. R. 21 2006 Small cap decouplings. With an appendix by D. R. Heath-Brown. Zbl 1454.42008 Demeter, Ciprian; Guth, Larry; Wang, Hong 20 2020 An estimate for Heilbronn’s exponential sum. Zbl 0857.11041 Heath-Brown, D. R. 20 1996 Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042 Heath-Brown, D. R. 19 2000 Primes represented by binary cubic forms. Zbl 1030.11046 Heath-Brown, D. R.; Moroz, B. Z. 17 2002 On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050 Heath-Brown, D. R.; Moroz, B. Z. 17 2004 The least square-free number in an arithmetic progression. Zbl 0493.10045 Heath-Brown, D. R. 16 1982 On simple zeros of the Riemann zeta-function. Zbl 1291.11118 Bui, H. M.; Heath-Brown, D. R. 16 2013 An asymptotic series for the mean value of Dirichlet \(L\)-functions. Zbl 0457.10020 Heath-Brown, D. R. 16 1981 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. 16 2008 Rational solutions of certain equations involving norms. Zbl 1023.11033 Heath-Brown, Roger; Skorobogatov, Alexei 16 2002 Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050 Heath-Brown, D. R.; Tolev, D. I. 16 2003 The first case of Fermat’s last theorem. Zbl 0557.10034 Adleman, L. M.; Heath-Brown, D. R. 15 1985 Small solutions of quadratic congruences. Zbl 0581.10008 Heath-Brown, D. R. 15 1985 The ternary Goldbach problem. Zbl 0599.10041 Heath-Brown, D. R. 15 1985 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. 14 2020 Square-free values of \(n^2+1\). Zbl 1312.11077 Heath-Brown, D. R. 14 2012 Odd perfect numbers. Zbl 0805.11005 Heath-Brown, D. R. 14 1994 On the density of the zeros of the Dedekind zeta-function. Zbl 0325.12003 Heath-Brown, D. R. 14 1977 On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055 Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E. 14 2005 The circle method and diagonal cubic forms. Zbl 0899.11051 Heath-Brown, D. R. 14 1998 Prime values of \(a^2 + p^4\). Zbl 1405.11124 Heath-Brown, D. R.; Li, Xiannan 14 2017 Arithmetic applications of Kloosterman sums. Zbl 1173.11339 Heath-Brown, D. R. 13 2000 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. 13 1985 Almost-prime \(k\)-tuples. Zbl 0886.11052 Heath-Brown, D. R. 13 1997 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. 13 2006 Power-free values of polynomials. Zbl 1287.11114 Heath-Brown, D. R. 12 2013 The largest prime factor of \(X^3+2\). Zbl 1023.11048 Heath-Brown, D. R. 12 2001 Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121 Heath-Brown, D. R.; Pierce, L. B. 12 2017 Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150 Heath-Brown, D. R. 12 2008 Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 1498.11233 Heath-Brown, David Rodney; Micheli, Giacomo 11 2019 Zeros of systems of \(\mathfrak p\)-adic quadratic forms. Zbl 1194.11047 Heath-Brown, D. R. 11 2010 Rational points on quartic hypersurfaces. Zbl 1169.11027 Browning, T. D.; Heath-Brown, D. R. 11 2009 A note on the Chevalley-Warning theorems. Zbl 1247.11089 Heath-Brown, D. R. 11 2011 Burgess’s bounds for character sums. Zbl 1328.11088 Heath-Brown, D. R. 11 2013 The density of zeros of forms for which weak approximation fails. Zbl 0778.11017 Heath-Brown, D. R. 11 1992 The differences between consecutive primes. Zbl 0387.10025 Heath-Brown, D. R. 11 1978 Almost-primes in short intervals. Zbl 0461.10041 Halberstam, H.; Heath-Brown, D. R.; Richert, H.-E. 11 1981 Siegel zeros and the least prime in an arithmetic progression. Zbl 0715.11049 Heath-Brown, D. R. 10 1990 Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031 Heath-Brown, D. R. 10 1993 The density of rational points on non-singular hypersurfaces. Zbl 0808.11042 Heath-Brown, D. R. 10 1994 The mean value theorem for the Riemann zeta-function. Zbl 0387.10023 Heath-Brown, D. R. 10 1979 Zero density estimates for the Riemann zeta-function and Dirichlet L-functions. Zbl 0393.10043 Heath-Brown, D. R. 10 1979 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. 10 1999 The density of rational points on Cayley’s cubic surface. Zbl 1060.11038 Heath-Brown, D. R. 9 2003 The density of rational points on non-singular hypersurfaces. I. Zbl 1174.11051 Browning, T. D.; Heath-Brown, D. R. 9 2006 Three primes and an almost-prime in arithmetic progression. Zbl 0425.10051 Heath-Brown, D. R. 9 1981 Quadratic class numbers divisible by 3. Zbl 1140.11050 Heath-Brown, D. Roger 9 2007 A note on the differences between consecutive primes. Zbl 0514.10031 Heath-Brown, D. R.; Goldston, D. A. 8 1984 Fractional moments of Dirichlet \(L\)-functions. Zbl 1248.11059 Heath-Brown, D. R. 8 2010 The differences between consecutive primes. II. Zbl 0394.10021 Heath-Brown, D. R. 8 1979 The cubic case of Vinogradov’s mean value theorem. Zbl 1522.11084 Heath-Brown, D. R. 2 2022 The geometric sieve for quadrics. Zbl 1481.11035 Browning, Tim D.; Heath-Brown, Roger 2 2021 The differences between consecutive primes. V. Zbl 1492.11136 Heath-Brown, Roger 1 2021 Small cap decouplings. With an appendix by D. R. Heath-Brown. Zbl 1454.42008 Demeter, Ciprian; Guth, Larry; Wang, Hong 20 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. 14 2020 Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 1498.11233 Heath-Brown, David Rodney; Micheli, Giacomo 11 2019 Counting rational points on quadric surfaces. Zbl 1444.11142 Browning, T. D.; Heath-Brown, D. R. 5 2018 Zeros of pairs of quadratic forms. Zbl 1405.11040 Heath-Brown, D. R. 4 2018 The differences between consecutive smooth numbers. Zbl 1446.11173 Heath-Brown, D. R. 3 2018 A new \(k\)th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110 Heath-Brown, D. R. 32 2017 Forms in many variables and differing degrees. Zbl 1383.11039 Browning, Tim; Heath-Brown, Roger 23 2017 Prime values of \(a^2 + p^4\). Zbl 1405.11124 Heath-Brown, D. R.; Li, Xiannan 14 2017 Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121 Heath-Brown, D. R.; Pierce, L. B. 12 2017 Averages and moments associated to class numbers of imaginary quadratic fields. Zbl 1391.11151 Heath-Brown, D. R.; Pierce, L. B. 7 2017 Iteration of quadratic polynomials over finite fields. Zbl 1428.11204 Heath-Brown, D. R. 5 2017 Almost prime triples and Chen’s theorem. Zbl 1390.11109 Heath-Brown, Roger; Li, Xiannan 4 2016 Small solutions of quadratic congruences, and character sums with binary quadratic forms. Zbl 1375.11036 Heath-Brown, D. R. 3 2016 Burgess bounds for short mixed character sums. Zbl 1317.11083 Heath-Brown, D. R.; Pierce, L. B. 8 2015 Rational points on intersections of cubic and quadric hypersurfaces. Zbl 1327.11043 Browning, T. D.; Dietmann, R.; Heath-Brown, D. R. 7 2015 Large gaps between consecutive prime numbers containing perfect powers. Zbl 1391.11125 Ford, Kevin; Heath-Brown, D. R.; Konyagin, Sergei 5 2015 On simple zeros of the Riemann zeta-function. Zbl 1291.11118 Bui, H. M.; Heath-Brown, D. R. 16 2013 Power-free values of polynomials. Zbl 1287.11114 Heath-Brown, D. R. 12 2013 Burgess’s bounds for character sums. Zbl 1328.11088 Heath-Brown, D. R. 11 2013 \(p\)-adic zeros of systems of quadratic forms. Zbl 1333.11036 Heath-Brown, D. R. 1 2013 Square-free values of \(n^2+1\). Zbl 1312.11077 Heath-Brown, D. R. 14 2012 Quadratic polynomials represented by norm forms. Zbl 1264.14032 Browning, T. D.; Heath-Brown, D. R. 8 2012 Counting rational points on smooth cyclic covers. Zbl 1248.14027 Heath-Brown, D. R.; Pierce, Lillian B. 7 2012 A note on the Chevalley-Warning theorems. Zbl 1247.11089 Heath-Brown, D. R. 11 2011 Artin’s conjecture on zeros of \(p\)-adic forms. Zbl 1243.11051 Heath-Brown, D. R. 1 2011 Pair correlation for fractional parts of \(\alpha n^2\). Zbl 1239.11081 Heath-Brown, D. R. 32 2010 Zeros of systems of \(\mathfrak p\)-adic quadratic forms. Zbl 1194.11047 Heath-Brown, D. R. 11 2010 Fractional moments of Dirichlet \(L\)-functions. Zbl 1248.11059 Heath-Brown, D. R. 8 2010 A note on the fourth moment of Dirichlet \(L\)-functions. Zbl 1203.11056 Bui, H. M.; Heath-Brown, D. R. 7 2010 Zeros of \(p\)-adic forms. Zbl 1233.11039 Heath-Brown, D. R. 7 2010 Bounds for the cubic Weyl sum. Zbl 1282.11102 Heath-Brown, D. R. 4 2010 Counting rational points on cubic curves. Zbl 1229.11052 Heath-Brown, Roger; Testa, Damiano 2 2010 Corrigendum to the paper “Quadratic class numbers divisible by 3”. Zbl 1214.11119 Heath-Brown, D. R. 1 2010 Rational points on quartic hypersurfaces. Zbl 1169.11027 Browning, T. D.; Heath-Brown, D. R. 11 2009 Integral points on cubic hypersurfaces. Zbl 1244.11066 Browning, T. D.; Heath-Brown, D. R. 6 2009 Convexity bounds for \(L\)-functions. Zbl 1169.11038 Heath-Brown, D. R. 5 2009 Sums and differences of three \(k\)th powers. Zbl 1182.11017 Heath-Brown, D. R. 4 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. 477 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. 16 2008 Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150 Heath-Brown, D. R. 12 2008 Cubic forms in 14 variables. Zbl 1135.11031 Heath-Brown, D. R. 28 2007 Quadratic class numbers divisible by 3. Zbl 1140.11050 Heath-Brown, D. Roger 9 2007 Carmichael numbers with three prime factors. Zbl 1151.11047 Heath-Brown, D. R. 6 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. 5 2007 Analytic methods for the distribution of rational points of algebraic varieties. Zbl 1181.11042 Heath-Brown, D. R. 2 2007 Counting rational points on algebraic varieties. Zbl 1098.14013 Browning, T. D.; Heath-Brown, D. R.; Salberger, P. 28 2006 Counting rational points on algebraic varieties. Zbl 1152.11027 Heath-Brown, D. R. 21 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. 13 2006 The density of rational points on non-singular hypersurfaces. I. Zbl 1174.11051 Browning, T. D.; Heath-Brown, D. R. 9 2006 Analytic number theory. Lectures given at the C.I.M.E. summer school held in Cetraro, Italy, July 11-18, 2002. Zbl 1098.11002 1 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 75 2005 Counting rational points on hypersurfaces. Zbl 1079.11033 Browning, T. D.; Heath-Brown, D. R. 21 2005 On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055 Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E. 14 2005 Plane curves in boxes and equal sums of two powers. Zbl 1174.11380 Browning, T. D.; Heath-Brown, D. R. 7 2005 Permutation groups, simple groups, and sieve methods. Zbl 1091.11035 Heath-Brown, D. R.; Praeger, Cheryl E.; Shalev, Aner 2 2005 Prime number theory and the Riemann zeta-function. Zbl 1204.11144 Heath-Brown, D. R. 1 2005 The average analytic rank of elliptic curves. Zbl 1063.11013 Heath-Brown, D. R. 31 2004 On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050 Heath-Brown, D. R.; Moroz, B. Z. 17 2004 Equal sums of three powers. Zbl 1135.11052 Browning, T. D.; Heath-Brown, D. R. 3 2004 Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050 Heath-Brown, D. R.; Tolev, D. I. 16 2003 The density of rational points on Cayley’s cubic surface. Zbl 1060.11038 Heath-Brown, D. R. 9 2003 Proceedings of the session in analytic number theory and Diophantine equations held in Bonn, Germany, January–June, 2002. Zbl 1050.11003 4 2003 Linear relations amongst sums of two squares. Zbl 1161.11387 Heath-Brown, D. R. 4 2003 Lectures on sieves. Zbl 1070.11045 Heath-Brown, D. R. 1 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. 96 2002 Integers represented as a sum of primes and powers of two. Zbl 1097.11050 Heath-Brown, D. R.; Puchta, J.-C. 41 2002 The distribution of \(\alpha p\) modulo one. Zbl 1023.11034 Heath-Brown, D. R.; Jia, Chaohua 21 2002 Primes represented by binary cubic forms. Zbl 1030.11046 Heath-Brown, D. R.; Moroz, B. Z. 17 2002 Rational solutions of certain equations involving norms. Zbl 1023.11033 Heath-Brown, Roger; Skorobogatov, Alexei 16 2002 Heilbronn’s exponential sum and transcendence theory. Zbl 1177.11072 Heath-Brown, D. R. 2 2002 Primes represented by \(x^3+ 2y^3\). Zbl 1007.11055 Heath-Brown, D. R. 37 2001 The largest prime factor of \(X^3+2\). Zbl 1023.11048 Heath-Brown, D. R. 12 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. 67 2000 Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042 Heath-Brown, D. R. 19 2000 Arithmetic applications of Kloosterman sums. Zbl 1173.11339 Heath-Brown, D. R. 13 2000 Exponential decay in the frequency of analytic ranks of automorphic \(L\)-functions. Zbl 1166.11326 Heath-Brown, D. R.; Michel, P. 4 2000 Lattice points in the sphere. Zbl 0929.11040 Heath-Brown, D. R. 62 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. 10 1999 The solubility of diagonal cubic Diophantine equations. Zbl 1029.11010 Heath-Brown, D. R. 4 1999 A note on the paper ‘consecutive almost-primes’. Zbl 1141.11318 Heath-Brown, D. R. 1 1999 The circle method and diagonal cubic forms. Zbl 0899.11051 Heath-Brown, D. R. 14 1998 The largest prime factor of the integers in an interval. II. Zbl 1066.11506 Heath-Brown, D. R.; Jia, Chaohua 4 1998 Counting rational points on cubic surfaces. Zbl 0926.11046 Heath-Brown, Roger 4 1998 The density of rational points on cubic surfaces. Zbl 0863.11021 Heath-Brown, D. R. 25 1997 Almost-prime \(k\)-tuples. Zbl 0886.11052 Heath-Brown, D. R. 13 1997 A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049 Heath-Brown, D. R. 86 1996 An estimate for Heilbronn’s exponential sum. Zbl 0857.11041 Heath-Brown, D. R. 20 1996 The largest prime factor of the integers in an interval. Zbl 0867.11064 Heath-Brown, D. R. 2 1996 A mean value estimate for real character sums. Zbl 0828.11040 Heath-Brown, D. R. 83 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. 77 1994 Sign changes of \(E(T)\), \(\Delta(x)\), and \(P(x)\). Zbl 0810.11046 Heath-Brown, D. R.; Tsang, K.-M. 23 1994 Odd perfect numbers. Zbl 0805.11005 Heath-Brown, D. R. 14 1994 The density of rational points on non-singular hypersurfaces. Zbl 0808.11042 Heath-Brown, D. R. 10 1994 The size of Selmer groups for the congruent number problem. Zbl 0808.11041 Heath-Brown, D. R. 37 1993 Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031 Heath-Brown, D. R. 10 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. 7 1993 ...and 74 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,696 Authors 75 Shparlinski, Igor E. 44 Browning, Timothy Daniel 39 Heath-Brown, Roger 32 Zhai, Wenguang 26 Wooley, Trevor D. 21 Lu, Guangshi 20 Ivić, Aleksandar 20 Michel, Philippe Gabriel 19 Blomer, Valentin 19 Harman, Glyn 19 Iwaniec, Henryk 18 Li, Jinjiang 17 Brüdern, Jörg 17 Fouvry, Etienne 17 Goldston, Daniel Alan 17 Soundararajan, Kannan 17 Zhang, Min 16 Baier, Stephan 16 Pintz, Janos 16 Zaharescu, Alexandru 16 Zhao, Liangyi 15 Baker, Roger C. 15 de la Bretèche, Régis 15 Young, Matthew P. 14 Gao, Peng 14 Kowalski, Emmanuel 14 Matomäki, Kaisa 14 Pierce, Lillian B. 14 Radziwiłł, Maksym 13 Dimitrov, Stoyan Ivanov 13 Hua, Guodong 13 Murty, Maruti Ram 13 Sankaranarayanan, Ayyadurai 13 Tao, Terence 12 Banks, William David 12 Bourgain, Jean 12 Cao, Xiaodong 12 Friedlander, John Benjamin 12 Laurinčikas, Antanas 12 Tsang, Kai-Man 11 Cai, Yingchun 11 Cochrane, Todd 11 Dietmann, Rainer 11 Hu, Liqun 11 Liu, Huafeng 11 Sawin, William F. 11 Xiao, Stanley Yao 10 Liu, Zhixin 10 Maynard, James 10 Munshi, Ritabrata 10 Perelli, Alberto 10 Pollack, Paul 10 Shkredov, Il’ya Dmitrievich 10 Steuding, Jörn 10 Tanigawa, Yoshio 10 Teräväinen, Joni 10 Wu, Jie 10 Zhao, Lilu 9 Bazzanella, Danilo 9 Brandes, Julia 9 Bui, Hung Manh 9 Chamizo Lorente, Fernando 9 Conrey, John Brian 9 Derenthal, Ulrich 9 Garaev, Moubariz Z. 9 Keating, Jonathan Peter 9 Konyagin, Sergeĭ Vladimirovich 9 Korolëv, Maksim Aleksandrovich 9 Sofos, Efthymios 8 Chang, Mei-Chu 8 Fomenko, Oleg Mstislavovich 8 Guo, Victor Zhenyu 8 Kerr, Bryce 8 Khan, Rizwanur 8 Koymans, Peter 8 Lamzouri, Youness 8 Lau, Yuk-Kam 8 Munsch, Marc 8 Nowak, Werner Georg 8 Salberger, Per 8 Schindler, Damaris 8 Singh, Saurabh Kumar 8 Thorner, Jesse 8 Wood, Melanie Matchett 8 Wu, Xiaosheng 8 Zaman, Asif 7 Aistleitner, Christoph 7 Chan, Tsz Ho 7 Ford, Kevin B. 7 Kumchev, Angel V. 7 Lao, Huixue 7 Liu, Huaning 7 Liu, Jianya 7 Luca, Florian 7 Milićević, Djordje 7 Milinovich, Micah B. 7 Ostafe, Alina 7 Pratt, Kyle 7 Rassias, Michael Th. 7 Rivat, Joël ...and 1,596 more Authors all top 5 Cited in 251 Serials 230 Journal of Number Theory 94 Mathematika 74 International Journal of Number Theory 71 Acta Arithmetica 58 The Ramanujan Journal 45 Mathematische Zeitschrift 44 Mathematische Annalen 44 Transactions of the American Mathematical Society 41 Monatshefte für Mathematik 41 Journal de Théorie des Nombres de Bordeaux 40 Proceedings of the American Mathematical Society 39 Duke Mathematical Journal 38 Mathematics of Computation 38 Functiones et Approximatio. 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Serie V 6 Forum of Mathematics, Pi 6 Research in the Mathematical Sciences 5 The Mathematical Intelligencer 5 Acta Mathematica 5 Bulletin de la Société Mathématique de France 5 Journal of Combinatorial Theory. Series A 5 Journal of Soviet Mathematics 5 Science in China. Series A 5 Expositiones Mathematicae 5 Selecta Mathematica. New Series 5 European Journal of Mathematics 4 Indian Journal of Pure & Applied Mathematics 4 Russian Mathematical Surveys 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Journal of Algebra 4 Rendiconti del Seminario Matematico della Università di Padova 4 Theoretical Computer Science 4 Combinatorica 4 Chinese Annals of Mathematics. Series B 4 Journal of Complexity 4 Taiwanese Journal of Mathematics 4 Journal of Integer Sequences 4 Portugaliae Mathematica. Nova Série ...and 151 more Serials all top 5 Cited in 49 Fields 2,082 Number theory (11-XX) 246 Algebraic geometry (14-XX) 63 Combinatorics (05-XX) 43 Dynamical systems and ergodic theory (37-XX) 40 Group theory and generalizations (20-XX) 38 Harmonic analysis on Euclidean spaces (42-XX) 36 Probability theory and stochastic processes (60-XX) 30 Information and communication theory, circuits (94-XX) 25 Partial differential equations (35-XX) 24 Computer science (68-XX) 21 Field theory and polynomials (12-XX) 21 Convex and discrete geometry (52-XX) 18 Linear and multilinear algebra; matrix theory (15-XX) 17 Global analysis, analysis on manifolds (58-XX) 14 Topological groups, Lie groups (22-XX) 13 History and biography (01-XX) 13 Quantum theory (81-XX) 11 Numerical analysis (65-XX) 10 Functions of a complex variable (30-XX) 10 Several complex variables and analytic spaces (32-XX) 9 Commutative algebra (13-XX) 9 Measure and integration (28-XX) 9 Approximations and expansions (41-XX) 8 General and overarching topics; collections (00-XX) 8 Mathematical logic and foundations (03-XX) 8 Special functions (33-XX) 7 Abstract harmonic analysis (43-XX) 7 Geometry (51-XX) 6 Associative rings and algebras (16-XX) 5 Real functions (26-XX) 5 Differential geometry (53-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Functional analysis (46-XX) 4 Manifolds and cell complexes (57-XX) 4 Statistics (62-XX) 4 Fluid mechanics (76-XX) 2 \(K\)-theory (19-XX) 2 Potential theory (31-XX) 2 Ordinary differential equations (34-XX) 2 Operator theory (47-XX) 2 Relativity and gravitational theory (83-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 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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