Edit Profile (opens in new tab) Heath-Brown, Roger Compute Distance To: Compute 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: 186 Publications since 1974 5 Contributions as Editor · 8 Further Contributions Reviewing Activity: 728 Reviews Biographic References: 1 Publication Co-Authors: 48 Co-Authors with 60 Joint Publications 1,615 Co-Co-Authors all top 5 Co-Authors 129 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 all top 5 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 1 Essential Number Theory all top 5 Fields 192 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 166 Publications have been cited 2,370 times in 1,777 Documents Cited by ▼ Year ▼ The theory of the Riemann zeta-function. 2nd ed., rev. by D. R. Heath-Brown. Zbl 0601.10026Titchmarsh, E. C. 930 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 1159.11001Hardy, G. H.; Wright, E. M. 344 2008 The Pjateckii-Sapiro prime number theorem. Zbl 0513.10042Heath-Brown, D. R. 83 1983 Artin’s conjecture for primitive roots. Zbl 0586.10025Heath-Brown, D. R. 78 1986 The fourth power moment of the Riemann zeta function. Zbl 0403.10018Heath-Brown, D. R. 78 1979 The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène). Zbl 1039.11044Heath-Brown, D. R. 72 2002 Prime numbers in short intervals and a generalized Vaughan identity. Zbl 0478.10024Heath-Brown, D. R. 71 1982 New bounds for Gauss sums derived from \(k\)th powers, and for Heilbronn’s exponential sum. Zbl 0983.11052Heath-Brown, D. R.; Konyagin, S. 61 2000 Zero-free regions for Dirichlet \(L\)-functions and the least prime in an arithmetic progression. Zbl 0739.11033Heath-Brown, D. R. 61 1992 The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Zbl 0815.11032Heath-Brown, D. R. 59 1994 A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049Heath-Brown, D. R. 58 1996 The twelfth power moment of the Riemann-function. Zbl 0394.10020Heath-Brown, D. R. 54 1978 A mean value estimate for real character sums. Zbl 0828.11040Heath-Brown, D. R. 53 1995 Lattice points in the sphere. Zbl 0929.11040Heath-Brown, D. R. 50 1999 Integer sets containing no arithmetic progressions. Zbl 0589.10062Heath-Brown, D. R. 47 1987 The distribution and moments of the error term in the Dirichlet divisor problems. Zbl 0725.11045Heath-Brown, D. R. 46 1992 Fractional moments of the Riemann zeta-function. Zbl 0431.10024Heath-Brown, D. R. 43 1981 The square sieve and consecutive square-free numbers. Zbl 0514.10038Heath-Brown, D. R. 40 1984 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 1125.11018Davenport, Harold 38 2005 Cubic forms in 10 variables. Zbl 0494.10012Heath-Brown, D. R. 35 1983 Hybrid bounds for Dirichlet L-functions. Zbl 0362.10035Heath-Brown, D. R. 35 1978 Integers represented as a sum of primes and powers of two. Zbl 1097.11050Heath-Brown, D. R.; Puchta, J.-C. 32 2002 Hybrid bounds for Dirichlet L-functions. II. Zbl 0396.10030Heath-Brown, D. R. 30 1980 Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. Zbl 0549.10030Balasubramanian, R.; Conrey, J. B.; Heath-Brown, D. R. 29 1985 The size of Selmer groups for the congruent number problem. Zbl 0808.11041Heath-Brown, D. R. 29 1993 The distribution of Kummer sums at prime arguments. Zbl 0412.10028Heath-Brown, D. R.; Patterson, S. J. 29 1979 The divisor function \(d_ 3(n)\) in arithmetic progressions. Zbl 0549.10034Heath-Brown, D. R. 28 1986 The number of primes in a short interval. Zbl 0646.10032Heath-Brown, D. R. 28 1988 Pair correlation for fractional parts of \(\alpha n^2\). Zbl 1239.11081Heath-Brown, D. R. 28 2010 Diophantine approximation with square-free numbers. Zbl 0539.10026Heath-Brown, D. R. 27 1984 The average analytic rank of elliptic curves. Zbl 1063.11013Heath-Brown, D. R. 25 2004 Almost-primes in arithmetic progressions and short intervals. Zbl 0375.10027Heath-Brown, D. R. 25 1978 Primes represented by \(x^3+ 2y^3\). Zbl 1007.11055Heath-Brown, D. R. 23 2001 Simple zeros of the Riemann zeta-function on the critical line. Zbl 0409.10027Heath-Brown, D. R. 23 1979 On the difference between consecutive primes. Zbl 0424.10028Heath-Brown, D. R.; Iwaniec, H. 23 1979 Cubic forms in 14 variables. Zbl 1135.11031Heath-Brown, D. R. 23 2007 Counting rational points on algebraic varieties. Zbl 1098.14013Browning, T. D.; Heath-Brown, D. R.; Salberger, P. 22 2006 The growth rate of the Dedekind zeta-function on the critical line. Zbl 0583.12011Heath-Brown, D. R. 22 1988 The density of rational points on cubic surfaces. Zbl 0863.11021Heath-Brown, D. R. 21 1997 Prime twins and Siegel zeros. Zbl 0517.10044Heath-Brown, D. R. 21 1983 Gaps between primes, and the pair correlation of zeros of the zeta-function. Zbl 0414.10044Heath-Brown, D. R. 21 1982 A new \(k\)th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110Heath-Brown, D. R. 20 2017 Weyl’s inequality, Hua’s inequality and Waring’s problem. Zbl 0619.10046Heath-Brown, D. R. 20 1988 The divisor function at consecutive integers. Zbl 0529.10040Heath-Brown, D. R. 19 1984 Counting rational points on hypersurfaces. Zbl 1079.11033Browning, T. D.; Heath-Brown, D. R. 18 2005 Sign changes of \(E(T)\), \(\Delta(x)\), and \(P(x)\). Zbl 0810.11046Heath-Brown, D. R.; Tsang, K.-M. 18 1994 An estimate for Heilbronn’s exponential sum. Zbl 0857.11041Heath-Brown, D. R. 17 1996 The distribution of \(\alpha p\) modulo one. Zbl 1023.11034Heath-Brown, D. R.; Jia, Chaohua 17 2002 The fourth power mean of Dirichlet’s L-functions. Zbl 0479.10027Heath-Brown, D. R. 17 1981 Counting rational points on algebraic varieties. Zbl 1152.11027Heath-Brown, D. R. 16 2006 Rational solutions of certain equations involving norms. Zbl 1023.11033Heath-Brown, Roger; Skorobogatov, Alexei 15 2002 Forms in many variables and differing degrees. Zbl 1383.11039Browning, Tim; Heath-Brown, Roger 15 2017 Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E. 15 2008 Small solutions of quadratic congruences. Zbl 0581.10008Heath-Brown, D. R. 15 1985 The least square-free number in an arithmetic progression. Zbl 0493.10045Heath-Brown, D. R. 14 1982 Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050Heath-Brown, D. R.; Tolev, D. I. 14 2003 On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050Heath-Brown, D. R.; Moroz, B. Z. 14 2004 An asymptotic series for the mean value of Dirichlet \(L\)-functions. Zbl 0457.10020Heath-Brown, D. R. 14 1981 Odd perfect numbers. Zbl 0805.11005Heath-Brown, D. R. 13 1994 Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042Heath-Brown, D. R. 13 2000 On the density of the zeros of the Dedekind zeta-function. Zbl 0325.12003Heath-Brown, D. R. 13 1977 On simple zeros of the Riemann zeta-function. Zbl 1291.11118Bui, H. M.; Heath-Brown, D. R. 13 2013 On the distribution of gaps between zeros of the zeta-function. Zbl 0557.10028Conrey, J. B.; Ghosh, A.; Goldston, D.; Gonek, S. M.; Heath-Brown, D. R. 12 1985 The first case of Fermat’s last theorem. Zbl 0557.10034Adleman, L. M.; Heath-Brown, D. R. 12 1985 Almost-prime \(k\)-tuples. Zbl 0886.11052Heath-Brown, D. R. 12 1997 Burgess’s bounds for character sums. Zbl 1328.11088Heath-Brown, D. R. 11 2013 Primes represented by binary cubic forms. Zbl 1030.11046Heath-Brown, D. R.; Moroz, B. Z. 10 2002 The largest prime factor of \(X^3+2\). Zbl 1023.11048Heath-Brown, D. R. 10 2001 Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031Heath-Brown, D. R. 10 1993 On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E. 10 2005 Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 1498.11233Heath-Brown, David Rodney; Micheli, Giacomo 9 2019 The circle method and diagonal cubic forms. Zbl 0899.11051Heath-Brown, D. R. 9 1998 Rational points on quartic hypersurfaces. Zbl 1169.11027Browning, T. D.; Heath-Brown, D. R. 9 2009 Siegel zeros and the least prime in an arithmetic progression. Zbl 0715.11049Heath-Brown, D. R. 9 1990 The mean value theorem for the Riemann zeta-function. Zbl 0387.10023Heath-Brown, D. R. 9 1979 The differences between consecutive primes. Zbl 0387.10025Heath-Brown, D. R. 9 1978 Zero density estimates for the Riemann zeta-function and Dirichlet L-functions. Zbl 0393.10043Heath-Brown, D. R. 9 1979 Three primes and an almost-prime in arithmetic progression. Zbl 0425.10051Heath-Brown, D. R. 9 1981 Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150Heath-Brown, D. R. 9 2008 A note on the differences between consecutive primes. Zbl 0514.10031Heath-Brown, D. R.; Goldston, D. A. 8 1984 The density of rational points on Cayley’s cubic surface. Zbl 1060.11038Heath-Brown, D. R. 8 2003 The density of zeros of forms for which weak approximation fails. Zbl 0778.11017Heath-Brown, D. R. 8 1992 The density of rational points on non-singular hypersurfaces. Zbl 0808.11042Heath-Brown, D. R. 8 1994 Square-free values of \(n^2+1\). Zbl 1312.11077Heath-Brown, D. R. 8 2012 Arithmetic applications of Kloosterman sums. Zbl 1173.11339Heath-Brown, D. R. 8 2000 The differences between consecutive primes. II. Zbl 0394.10021Heath-Brown, D. R. 8 1979 The density of rational points on non-singular hypersurfaces. II. (With an appendix by J. M. Starr). Zbl 1104.11015Browning, T. D.; Heath-Brown, D. R.; Starr, J. M. 8 2006 Zeros of \(p\)-adic forms. Zbl 1233.11039Heath-Brown, D. R. 8 2010 Zeros of systems of \(\mathfrak p\)-adic quadratic forms. Zbl 1194.11047Heath-Brown, D. R. 8 2010 Almost-primes in short intervals. Zbl 0461.10041Halberstam, H.; Heath-Brown, D. R.; Richert, H.-E. 8 1981 Burgess bounds for short mixed character sums. Zbl 1317.11083Heath-Brown, D. R.; Pierce, L. B. 8 2015 Quadratic polynomials represented by norm forms. Zbl 1264.14032Browning, T. D.; Heath-Brown, D. R. 7 2012 Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121Heath-Brown, D. R.; Pierce, L. B. 7 2017 Prime values of \(a^2 + p^4\). Zbl 1405.11124Heath-Brown, D. R.; Li, Xiannan 7 2017 The ternary Goldbach problem. Zbl 0599.10041Heath-Brown, D. R. 7 1985 Quadratic class numbers divisible by 3. Zbl 1140.11050Heath-Brown, D. Roger 7 2007 On solving the diophantine equation \(x^ 3+y^ 3+z^ 3=k\) on a vector computer. Zbl 0783.11046Heath-Brown, D. R.; Lioen, W. M.; te Riele, Herman J. J. 6 1993 Proceedings of the session in analytic number theory and Diophantine equations held in Bonn, Germany, January–June, 2002. Zbl 1050.11003 6 2003 The density of rational points on the cubic surface \(X_0^3=X_1X_2X_3\). Zbl 0938.11016Heath-Brown, D. R.; Moroz, B. Z. 6 1999 A note on the Chevalley-Warning theorems. Zbl 1247.11089Heath-Brown, D. R. 6 2011 The geometric sieve for quadrics. Zbl 1481.11035Browning, Tim D.; Heath-Brown, Roger 1 2021 Small cap decouplings. With an appendix by D. R. Heath-Brown. Zbl 1454.42008Demeter, Ciprian; Guth, Larry; Wang, Hong 4 2020 Density of rational points on a quadric bundle in \(\mathbb{P}^3 \times \mathbb{P}^3 \). Zbl 1477.11058Browning, T. D.; Heath-Brown, D. R. 2 2020 Irreducible polynomials over finite fields produced by composition of quadratics. Zbl 1498.11233Heath-Brown, David Rodney; Micheli, Giacomo 9 2019 Counting rational points on quadric surfaces. Zbl 1444.11142Browning, T. D.; Heath-Brown, D. R. 4 2018 The differences between consecutive smooth numbers. Zbl 1446.11173Heath-Brown, D. R. 1 2018 A new \(k\)th derivative estimate for exponential sums via Vinogradov’s mean value. Zbl 1461.11110Heath-Brown, D. R. 20 2017 Forms in many variables and differing degrees. Zbl 1383.11039Browning, Tim; Heath-Brown, Roger 15 2017 Simultaneous integer values of pairs of quadratic forms. Zbl 1396.11121Heath-Brown, D. R.; Pierce, L. B. 7 2017 Prime values of \(a^2 + p^4\). Zbl 1405.11124Heath-Brown, D. R.; Li, Xiannan 7 2017 Iteration of quadratic polynomials over finite fields. Zbl 1428.11204Heath-Brown, D. R. 4 2017 Averages and moments associated to class numbers of imaginary quadratic fields. Zbl 1391.11151Heath-Brown, D. R.; Pierce, L. B. 4 2017 Small solutions of quadratic congruences, and character sums with binary quadratic forms. Zbl 1375.11036Heath-Brown, D. R. 3 2016 Almost prime triples and Chen’s theorem. Zbl 1390.11109Heath-Brown, Roger; Li, Xiannan 2 2016 Burgess bounds for short mixed character sums. Zbl 1317.11083Heath-Brown, D. R.; Pierce, L. B. 8 2015 Rational points on intersections of cubic and quadric hypersurfaces. Zbl 1327.11043Browning, T. D.; Dietmann, R.; Heath-Brown, D. R. 6 2015 Large gaps between consecutive prime numbers containing perfect powers. Zbl 1391.11125Ford, Kevin; Heath-Brown, D. R.; Konyagin, Sergei 3 2015 On simple zeros of the Riemann zeta-function. Zbl 1291.11118Bui, H. M.; Heath-Brown, D. R. 13 2013 Burgess’s bounds for character sums. Zbl 1328.11088Heath-Brown, D. R. 11 2013 Power-free values of polynomials. Zbl 1287.11114Heath-Brown, D. R. 6 2013 \(p\)-adic zeros of systems of quadratic forms. Zbl 1333.11036Heath-Brown, D. R. 1 2013 Square-free values of \(n^2+1\). Zbl 1312.11077Heath-Brown, D. R. 8 2012 Quadratic polynomials represented by norm forms. Zbl 1264.14032Browning, T. D.; Heath-Brown, D. R. 7 2012 Counting rational points on smooth cyclic covers. Zbl 1248.14027Heath-Brown, D. R.; Pierce, Lillian B. 4 2012 A note on the Chevalley-Warning theorems. Zbl 1247.11089Heath-Brown, D. R. 6 2011 Pair correlation for fractional parts of \(\alpha n^2\). Zbl 1239.11081Heath-Brown, D. R. 28 2010 Zeros of \(p\)-adic forms. Zbl 1233.11039Heath-Brown, D. R. 8 2010 Zeros of systems of \(\mathfrak p\)-adic quadratic forms. Zbl 1194.11047Heath-Brown, D. R. 8 2010 A note on the fourth moment of Dirichlet \(L\)-functions. Zbl 1203.11056Bui, H. M.; Heath-Brown, D. R. 4 2010 Fractional moments of Dirichlet \(L\)-functions. Zbl 1248.11059Heath-Brown, D. R. 4 2010 Bounds for the cubic Weyl sum. Zbl 1282.11102Heath-Brown, D. R. 3 2010 Counting rational points on cubic curves. Zbl 1229.11052Heath-Brown, Roger; Testa, Damiano 1 2010 Rational points on quartic hypersurfaces. Zbl 1169.11027Browning, T. D.; Heath-Brown, D. R. 9 2009 Integral points on cubic hypersurfaces. Zbl 1244.11066Browning, T. D.; Heath-Brown, D. R. 6 2009 Sums and differences of three \(k\)th powers. Zbl 1182.11017Heath-Brown, D. R. 3 2009 Convexity bounds for \(L\)-functions. Zbl 1169.11038Heath-Brown, D. R. 3 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 1159.11001Hardy, G. H.; Wright, E. M. 344 2008 Density of non-residues in Burgess-type intervals and applications. Zbl 1229.11006Banks, W. D.; Garaev, M. Z.; Heath-Brown, D. R.; Shparlinski, I. E. 15 2008 Imaginary quadratic fields with class group exponent 5. Zbl 1268.11150Heath-Brown, D. R. 9 2008 Cubic forms in 14 variables. Zbl 1135.11031Heath-Brown, D. R. 23 2007 Quadratic class numbers divisible by 3. Zbl 1140.11050Heath-Brown, D. Roger 7 2007 Every sum of cubes in \(\mathbb F_2[t]\) is a strict sum of 6 cubes. Zbl 1172.11045Gallardo, Luis H.; Heath-Brown, D. R. 5 2007 Carmichael numbers with three prime factors. Zbl 1151.11047Heath-Brown, D. R. 3 2007 Analytic methods for the distribution of rational points of algebraic varieties. Zbl 1181.11042Heath-Brown, D. R. 2 2007 Counting rational points on algebraic varieties. Zbl 1098.14013Browning, T. D.; Heath-Brown, D. R.; Salberger, P. 22 2006 Counting rational points on algebraic varieties. Zbl 1152.11027Heath-Brown, D. R. 16 2006 The density of rational points on non-singular hypersurfaces. II. (With an appendix by J. M. Starr). Zbl 1104.11015Browning, T. D.; Heath-Brown, D. R.; Starr, J. M. 8 2006 The density of rational points on non-singular hypersurfaces. I. Zbl 1174.11051Browning, T. D.; Heath-Brown, D. R. 4 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 1125.11018Davenport, Harold 38 2005 Counting rational points on hypersurfaces. Zbl 1079.11033Browning, T. D.; Heath-Brown, D. R. 18 2005 On the average value of divisor sums in arithmetic progressions. Zbl 1071.11055Banks, William D.; Heath-Brown, Roger; Shparlinski, Igor E. 10 2005 Plane curves in boxes and equal sums of two powers. Zbl 1174.11380Browning, T. D.; Heath-Brown, D. R. 5 2005 Permutation groups, simple groups, and sieve methods. Zbl 1091.11035Heath-Brown, D. R.; Praeger, Cheryl E.; Shalev, Aner 2 2005 Prime number theory and the Riemann zeta-function. Zbl 1204.11144Heath-Brown, D. R. 1 2005 The average analytic rank of elliptic curves. Zbl 1063.11013Heath-Brown, D. R. 25 2004 On the representation of primes by cubic polynomials in two variables. Zbl 1099.11050Heath-Brown, D. R.; Moroz, B. Z. 14 2004 Equal sums of three powers. Zbl 1135.11052Browning, T. D.; Heath-Brown, D. R. 1 2004 Lagrange’s four squares theorem with one prime and three almost-prime variables. Zbl 1022.11050Heath-Brown, D. R.; Tolev, D. I. 14 2003 The density of rational points on Cayley’s cubic surface. Zbl 1060.11038Heath-Brown, D. R. 8 2003 Proceedings of the session in analytic number theory and Diophantine equations held in Bonn, Germany, January–June, 2002. Zbl 1050.11003 6 2003 Linear relations amongst sums of two squares. Zbl 1161.11387Heath-Brown, D. R. 4 2003 Lectures on sieves. Zbl 1070.11045Heath-Brown, D. R. 1 2003 The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène). Zbl 1039.11044Heath-Brown, D. R. 72 2002 Integers represented as a sum of primes and powers of two. Zbl 1097.11050Heath-Brown, D. R.; Puchta, J.-C. 32 2002 The distribution of \(\alpha p\) modulo one. Zbl 1023.11034Heath-Brown, D. R.; Jia, Chaohua 17 2002 Rational solutions of certain equations involving norms. Zbl 1023.11033Heath-Brown, Roger; Skorobogatov, Alexei 15 2002 Primes represented by binary cubic forms. Zbl 1030.11046Heath-Brown, D. R.; Moroz, B. Z. 10 2002 Heilbronn’s exponential sum and transcendence theory. Zbl 1177.11072Heath-Brown, D. R. 2 2002 Primes represented by \(x^3+ 2y^3\). Zbl 1007.11055Heath-Brown, D. R. 23 2001 The largest prime factor of \(X^3+2\). Zbl 1023.11048Heath-Brown, D. R. 10 2001 New bounds for Gauss sums derived from \(k\)th powers, and for Heilbronn’s exponential sum. Zbl 0983.11052Heath-Brown, D. R.; Konyagin, S. 61 2000 Kummer’s conjecture for cubic Gauss sums. Zbl 0989.11042Heath-Brown, D. R. 13 2000 Arithmetic applications of Kloosterman sums. Zbl 1173.11339Heath-Brown, D. R. 8 2000 Exponential decay in the frequency of analytic ranks of automorphic \(L\)-functions. Zbl 1166.11326Heath-Brown, D. R.; Michel, P. 4 2000 Lattice points in the sphere. Zbl 0929.11040Heath-Brown, D. R. 50 1999 The density of rational points on the cubic surface \(X_0^3=X_1X_2X_3\). Zbl 0938.11016Heath-Brown, D. R.; Moroz, B. Z. 6 1999 The solubility of diagonal cubic Diophantine equations. Zbl 1029.11010Heath-Brown, D. R. 4 1999 A note on the paper ‘consecutive almost-primes’. Zbl 1141.11318Heath-Brown, D. R. 1 1999 The circle method and diagonal cubic forms. Zbl 0899.11051Heath-Brown, D. R. 9 1998 The largest prime factor of the integers in an interval. II. Zbl 1066.11506Heath-Brown, D. R.; Jia, Chaohua 3 1998 Counting rational points on cubic surfaces. Zbl 0926.11046Heath-Brown, Roger 2 1998 The density of rational points on cubic surfaces. Zbl 0863.11021Heath-Brown, D. R. 21 1997 Almost-prime \(k\)-tuples. Zbl 0886.11052Heath-Brown, D. R. 12 1997 A new form of the circle method, and its application to quadratic forms. Zbl 0857.11049Heath-Brown, D. R. 58 1996 An estimate for Heilbronn’s exponential sum. Zbl 0857.11041Heath-Brown, D. R. 17 1996 The largest prime factor of the integers in an interval. Zbl 0867.11064Heath-Brown, D. R. 2 1996 A mean value estimate for real character sums. Zbl 0828.11040Heath-Brown, D. R. 53 1995 The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Zbl 0815.11032Heath-Brown, D. R. 59 1994 Sign changes of \(E(T)\), \(\Delta(x)\), and \(P(x)\). Zbl 0810.11046Heath-Brown, D. R.; Tsang, K.-M. 18 1994 Odd perfect numbers. Zbl 0805.11005Heath-Brown, D. R. 13 1994 The density of rational points on non-singular hypersurfaces. Zbl 0808.11042Heath-Brown, D. R. 8 1994 The size of Selmer groups for the congruent number problem. Zbl 0808.11041Heath-Brown, D. R. 29 1993 Fractional moments of the Riemann zeta-function. II. Zbl 0798.11031Heath-Brown, D. R. 10 1993 On solving the diophantine equation \(x^ 3+y^ 3+z^ 3=k\) on a vector computer. Zbl 0783.11046Heath-Brown, D. R.; Lioen, W. M.; te Riele, Herman J. J. 6 1993 The Dirichlet divisor problem. Zbl 0791.11048Heath-Brown, D. R. 3 1993 Zero-free regions for Dirichlet \(L\)-functions and the least prime in an arithmetic progression. Zbl 0739.11033Heath-Brown, D. R. 61 1992 The distribution and moments of the error term in the Dirichlet divisor problems. Zbl 0725.11045Heath-Brown, D. R. 46 1992 The density of zeros of forms for which weak approximation fails. Zbl 0778.11017Heath-Brown, D. R. 8 1992 Calabi-Yau threefolds with \(\rho > 13\). Zbl 0759.14030Heath-Brown, D. R.; Wilson, P. M. H. 4 1992 Zero-free regions of \(\zeta (s)\) and \(L(s,\chi)\). Zbl 0791.11042Heath-Brown, D. R. 2 1992 ...and 66 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,393 Authors 60 Shparlinski, Igor E. 38 Browning, Timothy Daniel 35 Heath-Brown, Roger 28 Zhai, Wenguang 21 Wooley, Trevor D. 20 Ivić, Aleksandar 20 Lu, Guangshi 18 Harman, Glyn 18 Iwaniec, Henryk 16 Michel, Philippe Gabriel 15 Baier, Stephan 15 Blomer, Valentin 15 Fouvry, Etienne 15 Goldston, Daniel Alan 15 Zaharescu, Alexandru 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 Kowalski, Emmanuel 12 Murty, Maruti Ram 12 Tsang, Kai-Man 12 Zhang, Min 12 Zhao, Liangyi 11 Friedlander, John Benjamin 11 Laurinčikas, Antanas 11 Pintz, Janos 11 Soundararajan, Kannan 11 Tao, Terence 10 Cai, Yingchun 10 Cochrane, Todd 10 Dietmann, Rainer 10 Hu, Liqun 10 Liu, Zhixin 10 Munshi, Ritabrata 10 Perelli, Alberto 10 Pierce, Lillian B. 10 Radziwiłł, Maksym 10 Tanigawa, Yoshio 10 Young, Matthew P. 9 Bazzanella, Danilo 9 Conrey, John Brian 9 Gao, Peng 9 Garaev, Moubariz Z. 9 Liu, Huafeng 9 Wu, Jie 8 Brandes, Julia 8 Chamizo Lorente, Fernando 8 Chang, Mei-Chu 8 Fomenko, Oleg Mstislavovich 8 Keating, Jonathan Peter 8 Konyagin, Sergeĭ Vladimirovich 8 Lau, Yuk-Kam 8 Pollack, Paul 8 Sankaranarayanan, Ayyadurai 8 Sawin, William F. 8 Shkredov, Il’ya Dmitrievich 8 Steuding, Jörn 8 Vaughan, Robert C. 7 Derenthal, Ulrich 7 Dimitrov, Stoyan Ivanov 7 Ford, Kevin B. 7 Korolëv, Maksim Aleksandrovich 7 Kumchev, Angel V. 7 Luca, Florian 7 Maynard, James 7 Nowak, Werner Georg 7 Rassias, Michael Th. 7 Robles, Nicolas 7 Salberger, Per 7 Sarnak, Peter Clive 7 Xiao, Stanley Yao 7 Yamagishi, Shuntaro 7 Zhao, Lilu 6 Aistleitner, Christoph 6 Bui, Hung Manh 6 Gritsenko, Sergeĭ Aleksandrovich 6 Helfgott, Harald Andrés 6 Jutila, Matti Ilmari 6 Lamzouri, Youness 6 Maier, Helmut 6 Milićević, Djordje 6 Milinovich, Micah B. 6 Motohashi, Yoichi 6 Munsch, Marc 6 Parsell, Scott T. 6 Pratt, Kyle 6 Rivat, Joël 6 Rubin, Karl Cooper 6 Rudnick, Zeév 6 Schindler, Damaris 6 Sofos, Efthymios 6 Sono, Keiju 6 Sun, Haiwei 6 Tolev, Doychin I. 6 Xi, Ping 6 Zaman, Asif ...and 1,293 more Authors all top 5 Cited in 228 Serials 207 Journal of Number Theory 71 Mathematika 62 International Journal of Number Theory 46 Acta Arithmetica 39 Transactions of the American Mathematical Society 39 Journal de Théorie des Nombres de Bordeaux 38 Mathematics of Computation 38 Mathematische Zeitschrift 38 Proceedings of the American Mathematical Society 37 Monatshefte für Mathematik 36 Duke Mathematical Journal 32 Functiones et Approximatio. Commentarii Mathematici 32 Mathematische Annalen 32 The Ramanujan Journal 29 Advances in Mathematics 27 Algebra & Number Theory 26 Acta Mathematica Hungarica 25 Lithuanian Mathematical Journal 25 Mathematical Proceedings of the Cambridge Philosophical Society 24 Inventiones Mathematicae 23 Journal für die Reine und Angewandte Mathematik 23 Research in Number Theory 22 Rocky Mountain Journal of Mathematics 20 Compositio Mathematica 19 Israel Journal of Mathematics 18 Mathematical Notes 18 Annals of Mathematics. Second Series 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 15 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 Integers 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 Journal of the Australian Mathematical Society 8 Central European Journal of Mathematics 8 Discrete Analysis 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 Frontiers of Mathematics in China 6 Communications in Mathematical Physics 6 Canadian Journal of Mathematics 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 5 Research in the Mathematical Sciences 4 American Mathematical Monthly 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 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 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 Journal of Pure and Applied Algebra 3 Nagoya Mathematical Journal 3 Pacific Journal of Mathematics 3 Rendiconti del Seminario Matematico della Università di Padova 3 St. Petersburg Mathematical Journal ...and 128 more Serials all top 5 Cited in 47 Fields 1,669 Number theory (11-XX) 194 Algebraic geometry (14-XX) 54 Combinatorics (05-XX) 32 Dynamical systems and ergodic theory (37-XX) 29 Group theory and generalizations (20-XX) 25 Probability theory and stochastic processes (60-XX) 25 Information and communication theory, circuits (94-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 20 Partial differential equations (35-XX) 19 Convex and discrete geometry (52-XX) 17 Computer science (68-XX) 16 Field theory and polynomials (12-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 14 Global analysis, analysis on manifolds (58-XX) 12 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) 8 Approximations and expansions (41-XX) 7 Mathematical logic and foundations (03-XX) 7 Measure and integration (28-XX) 6 Geometry (51-XX) 5 General and overarching topics; collections (00-XX) 5 Commutative algebra (13-XX) 5 Associative rings and algebras (16-XX) 4 Abstract harmonic analysis (43-XX) 4 Differential geometry (53-XX) 4 Statistical mechanics, structure of matter (82-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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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