Roger Heath-Brown

Roger Heath-Brown's AcademicInfluence.com Rankings

Roger Heath-Brown

Mathematics

#1092

World Rank

#1855

Historical Rank

Number Theory

#51

World Rank

#77

Historical Rank

Measure Theory

#1002

World Rank

#1296

Historical Rank

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Mathematics

Why Is Roger Heath-Brown Influential?

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According to Wikipedia, David Rodney "Roger" Heath-Brown is a British mathematician working in the field of analytic number theory. Education He was an undergraduate and graduate student of Trinity College, Cambridge; his research supervisor was Alan Baker.

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Roger Heath-Brown's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The Theory of the Riemann Zeta-Function (1987) (3415)
The Ternary Goldbach Problem (1985) (277)
Zero-free regions for Dirichlet $L$-functions, and the least prime in an arithmetic progression (1992) (224)
The density of rational points on curves and surfaces (2002) (209)
A mean value estimate for real character sums (1995) (199)
Integer Sets Containing No Arithmetic Progressions (1987) (183)
Prime Numbers in Short Intervals and a Generalized Vaughan Identity (1982) (182)
ARTIN'S CONJECTURE FOR PRIMITIVE ROOTS (1986) (181)
A new form of the circle method, and its application to quadratic forms. (1996) (169)
The distribution and moments of the error term in the Dirichlet divisor problem Acta Arith (1992) (147)
The size of Selmer groups for the congruent number problem (1993) (139)
The Pjateckiĭ-S̆apiro prime number theorem (1983) (121)
Lattice points in the sphere (1999) (112)
Cubic Forms in Ten Variables (1983) (112)
The number of primes in a short interval. (1988) (109)
The Fourth Power Moment of the Riemann Zeta Function (1979) (109)
The average rank of elliptic curves (2004) (107)
The square sieve and consecutive square-free numbers (1984) (102)
The size of Selmer groups for the congruent number problem, II (1994) (101)
Counting Rational Points on Algebraic Varieties (2004) (90)
The distribution of Kummer sums at prime arguments. (1979) (89)
On the difference between consecutive primes (1979) (86)
Integers Represented as a Sum of Primes and Powers of Two (2002) (85)
THE TWELFTH POWER MOMENT OF THE RIEMANN-FUNCTION (1978) (82)
Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. (1985) (81)
The density of rational points on cubic surfaces (1997) (72)
The average analytic rank of elliptic curves (2003) (71)
Zeros of the Riemann Zeta-function on the critical line (1993) (68)
The divisor function $d_3(n)$ in arithmetic progressions (1986) (66)
Diophantine approximation with square-free numbers (1984) (65)
An estimate for Heilbronn's exponential sum (1996) (64)
Fractional Moments of the Riemann Zeta‐Function (1981) (63)
Simple Zeros of the Riemann Zeta-Function on the Critical Line (1979) (60)
Gaps between primes, and the pair correlation of zeros of the zeta-function (1982) (59)
Counting rational points on hypersurfaces (2004) (57)
Cubic forms in 14 variables (2007) (57)
Pair correlation for fractional parts of αn2 (2009) (55)
Odd perfect numbers (1994) (53)
The growth rate of the Dedekind Zeta-function on the critical line (1988) (52)
ON THE DISTRIBUTION OF GAPS BETWEEN ZEROS OF THE ZETA-FUNCTION (1985) (49)
The Fourth Power Mean of Dirichlet's L-Functions (1981) (48)
On the average value of divisor sums in arithmetic progressions (2005) (48)
Forms in many variables and differing degrees (2014) (47)
HYBRID BOUNDS FOR DIRICHLET L-FUNCTIONS II (1980) (47)
Rational solutions of certain equations involving norms (2002) (47)
Prime Twins and Siegel Zeros (1983) (43)
Weyl's Inequality, Hua's Inequality, and Waring's Problem (1988) (43)
The Density of Rational Points on Non‐Singular Hypersurfaces, I (2005) (42)
The circle method and diagonal cubic forms (1998) (41)
Sign Changes of E(T), Δ(x), and P(x) (1994) (39)
Hybrid bounds for DirichletL-functions (1978) (39)
Primes Represented by Binary Cubic Forms (2002) (37)
APPLICATIONS OF SIEVE METHODS TO THE THEORY OF NUMBERS (1980) (37)
The mean value theorem for the Riemann zeta-function (1978) (37)
The density of rational points on non-singular hypersurfaces (1994) (36)
The density of rational points on Cayley's cubic surface (2002) (35)
The density of zeros of forms for which weak approximation fails (1992) (34)
Lectures on sieves (2002) (34)
The divisor function at consecutive integers (1984) (33)
Almost-primes in arithmetic progressions and short intervals (1978) (33)
An asymptotic series for the mean value of DirichletL-functions (1981) (32)
Kummer’s conjecture for cubic Gauss sums (2000) (32)
Rational points on quartic hypersurfaces (2007) (32)
Primes Represented by x 3 + 2 y 3 (32)
VAN DER CORPUT'S METHOD OF EXPONENTIAL SUMS (London Mathematical Society Lecture Note Series 126) (1991) (31)
RANDOM MATRICES, FROBENIUS EIGENVALUES, AND MONODROMY (American Mathematical Society Colloquium Publications 45) By N ICHOLAS M. K ATZ and P ETER S ARNAK : 419 pp., US$69.00, ISBN 0 8218 1017 0 (American Mathematical Society, 1998). (2000) (31)
On the Representation of Primes by Cubic Polynomials in Two Variables (2004) (30)
The Differences between Consecutive Primes (1978) (30)
A note on the differences between consecutive primes (1984) (29)
The Distribution of αp Modulo One (2002) (28)
The first case of Fermat's last theorem (1985) (28)
On the density of the zeros of the Dedekind Zeta-function (1977) (28)
Square-free values of $n^2+1$ (2010) (27)
Zeros of p‐adic forms (2008) (27)
The Differences between Consecutive Primes, II (1979) (27)
Quadratic polynomials represented by norm forms (2011) (26)
The density of rational points on the cubic surface X30= X1X2X3 (1999) (25)
Zero Density Estimates for the Riemann Zeta‐Function and Dirichlet L‐Functions (1979) (25)
A new kth derivative estimate for exponential sums via Vinogradov’s mean value (2016) (25)
The least square-free number in an arithmetic progression. (1982) (25)
Number Theory and Algebraic Geometry: Linear relations amongst sums of two squares (2004) (25)
SIEGEL ZEROS AND THE LEAST PRIME IN AN ARITHMETIC PROGRESSION (1990) (24)
Arithmetic applications of Kloosterman sums (2000) (23)
FRACTIONAL MOMENTS OF THE RIEMANN ZETA-FUNCTION, II (1993) (23)
Density of non‐residues in Burgess‐type intervals and applications (2006) (22)
Irreducible polynomials over finite fields produced by composition of quadratics (2017) (22)
The largest prime factor of X3+2 (2001) (21)
Burgess's Bounds for Character Sums (2012) (21)
Simultaneous Integer Values of Pairs of Quadratic Forms (2013) (21)
Zeros of systems of 𝔭-adic quadratic forms (2010) (20)
Lagrange's four squares theorem with one prime and threealmost--prime variables (2003) (19)
The fractional part of αn k (1988) (19)
The first case of fermat’s last theorem (1985) (18)
Sums and differences of three kth powers (2008) (18)
Density of rational points on a quadric bundle in P 3 × P 3 (2018) (17)
Fermat's two squares theorem (1984) (16)
Convexity bounds for $L$-functions (2008) (16)
Fractional Moments of Dirichlet $L$-Functions (2009) (16)
Plane curves in boxes and equal sums of two powers (2005) (16)
Imaginary quadratic fields with class group exponent 5 (2008) (16)
Calabi-Yau threefolds with ρ>13 (1992) (16)
RATIONAL POINTS ON INTERSECTIONS OF CUBIC AND QUADRIC HYPERSURFACES (2013) (15)
Searching for Solutions of x 3 + y 3 + z 3 = k (1992) (15)
The Density of Zeros of Dirichlet's L-Functions (1979) (15)
On solving the diophantine equation $ x^ 3 + y^ 3 + z^ 3 = k $ on a vector computer (1991) (14)
Burgess bounds for short mixed character sums (2014) (14)
Averages and moments associated to class numbers of imaginary quadratic fields (2014) (13)
Small solutions of quadratic congruences (1985) (13)
The cubic case of Vinogradov’s mean value theorem (2015) (13)
Square-full numbers in short intervals (1991) (12)
Prime number theory and the Riemann Zeta-function (2005) (12)
A note on the fourth moment of Dirichlet L-functions (2009) (12)
Primes in ‘Almost All’ Short Intervals (1982) (11)
Power-free values of polynomials (2013) (11)
Almost-prime k-tuples (1997) (11)
The largest prime factor of the integers in an interval, II (1998) (11)
Counting rational points on smooth cyclic covers (2011) (11)
The Solubility of Diagonal Cubic Diophantine Equations (1999) (11)
Small solutions of quadratic congruences, II (1991) (10)
QUADRATIC CLASS NUMBERS DIVISIBLE BY 3 (2007) (10)
On solving the Diophantine equation ³+³+³= on a vector computer (1993) (10)
FERMAT'S LAST THEOREM FOR "ALMOST ALL" EXPONENTS (1985) (10)
Integral points on cubic hypersurfaces (2006) (10)
On simple zeros of the Riemann zeta‐function (2013) (10)
A Large Values Estimate for Dirichlet Polynomials (1979) (9)
Zeros of pairs of quadratic forms (2013) (8)
Counting Rational Points on Cubic Surfaces (2015) (8)
ANALYTIC METHODS FOR THE DISTRIBUTION OF RATIONAL POINTS ON ALGEBRAIC VARIETIES (2007) (8)
Cubic forms in 10 variables (1984) (8)
Bounds for the cubic Weyl sum (2009) (7)
Prime values of $$a^2 + p^4$$a2+p4 (2017) (7)
The geometric sieve for quadrics (2020) (7)
Powerfree Values of Polynomials (2011) (7)
The Differences Between Consecutive Smooth Numbers. (2018) (7)
ITERATION OF QUADRATIC POLYNOMIALS OVER FINITE FIELDS (2017) (6)
Equal sums of three powers (2004) (6)
Artin's Conjecture on Zeros of p-adic Forms (2010) (6)
The Differences Between Consecutive Primes. V (2019) (6)
Large gaps between consecutive prime numbers containing perfect powers (2014) (6)
Counting rational points on quadric surfaces (2018) (5)
A parity problem from sieve theory (1982) (5)
Exponential decay in the frequency of analytic ranks of automorphic L-functions (2000) (5)
Small solutions of quadratic congruences, and character sums with binary quadratic forms (2014) (5)
Permutation groups, simple groups, and sieve methods (2005) (5)
Counting rational points on cubic curves (2009) (5)
Every sum of cubes in F2[t] is a strict sum of 6 cubes (2007) (5)
A Tribute to Paul Erdős: The differences between consecutive primes, IV (1990) (5)
Carmichael number with three prime factors. (2007) (4)
Almost prime triples and Chen's Theorem (2015) (4)
Representation of an integer as a prime plus a product of two small factors (1981) (4)
Heilbronn's exponential sum and transcendence theory (2002) (4)
Weyl's inequality and hua's inequality (1989) (4)
A Multiple Exponential Sum to Modulus p 2 (1985) (3)
Edmund Landau: Collected Works (1989) (3)
On a paper of Baker and Schinzel (1979) (3)
RATIONAL POINTS ON INTERSECTIONS OF CUBIC AND QUADRIC HYPERSURFACES – CORRIGENDUM (2014) (2)
Zeros of systems of ${\mathfrak p}$-adic Quadratic Forms (2008) (2)
On solving the Diophantine equation $xsp 3+ysp 3+zsp 3=k$ on a vector computer (1993) (2)
Density of non-residues in short intervals (2006) (2)
Sieve identities and gaps between primes (2019) (1)
A note on the 2--part of Sha for the congruent number curves (2007) (1)
A pr 2 00 9 Zeros of Systems of p-adic Quadratic Forms (2009) (1)
IVAN MATVEEVIC VINOGRADOV: SELECTED WORKS (1986) (1)
Rational points on the intersection of three quadrics (2015) (1)
Simultaneous equal sums of three powers (2005) (1)
Searching for Salutions of x 3 + y3 + z3 = k (1992) (1)
The Differences Between Consecutive Primes, V (2019) (1)
Corrigendum to the paper ``Quadratic Class Numbers Divisible by 3'' (Functiones et Approximatio 37 (2007), 203--211) (2010) (1)
A new kth derivative estimate for exponential sums via Vinogradov’s mean value (2017) (1)
Sieves in Number Theory Lecture Notes Taught Course Centre 2007 (2009) (0)
J an 2 01 2 p-adic Zeros of Systems of Quadratic Forms (2013) (0)
The average elliptic curve has few integral points (2014) (0)
(2017). Forms in many variables and differing degrees. Journal of the European Mathematical Society , 19 (2), 357-394. (2015) (0)
Rational Points and Analytic Number Theory (2004) (0)
On large gaps between consecutive zeros, on the critical line, of some zeta-functions (2011) (0)
Quadratic polynomials represented by norm forms (2012) (0)
Mathematical people: Roger Heath-Brown (1991) (0)
Acknowledgment of priority (1996) (0)
Prizewinners 2009 (2010) (0)
A sieve problem over the Gaussian integers (2010) (0)
Study of rational cubic forms via the circle method [ after (2019) (0)
An Exciting Year on Analysis in Number Theory (2007) (0)
The average elliptic curve has few integral (2014) (0)
Primes represented by cubic forms (2002) (0)
Primes values of $a^2 + p^4$ (2015) (0)
Arithmetical Functions and Inversion Formulae (1974) (0)
The Distribution of Rational Points on Conics (2022) (0)
O ct 2 00 4 Counting Rational Points on Algebraic Varieties (2004) (0)
George Greaves, 1941–2008 (2011) (0)
Equidistribution for solutions of $p+m^2+n^2=N$, and for Châtelet surfaces (2022) (0)
A pr 2 00 4 Counting Rational Points on Hypersurfaces (2009) (0)
Komaravolu Chandrasekharan (1920–2017) (2018) (0)
Corrigendum --- Quadratic Class Numbers Divisible by 3 (2010) (0)
Topics in Analytic Number Theory (1985) (0)
2 2 A pr 2 00 5 Counting Rational Points on Algebraic Varieties (2008) (0)
Prime values of a2+p4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a^2 + p^4$$\end{document} (2016) (0)
Supplementary material from "CHRISTOPHER HOOLEY. 7 August 1928—;13 December 2018" (2020) (0)
Christopher Hooley. 7 August 1928—13 December 2018 (2020) (0)
DENSITY OF RATIONAL POINTS ON A QUADRIC BUNDLE IN P × P (2019) (0)
7 S ep 2 00 5 Simultaneous equal sums of three powers (0)
2 00 5 Counting Rational Points on Hypersurfaces (2009) (0)

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