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- D. R. Heath-Brown

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
40
Citations
10,356
140
World Ranking
1345
National Ranking
100

2016 - Member of Academia Europaea

2013 - Fellow of the American Mathematical Society

- Algebra
- Number theory
- Combinatorics

His main research concerns Combinatorics, Discrete mathematics, Prime, Pure mathematics and Arithmetic. The Combinatorics study combines topics in areas such as Zero and Surface. D. R. Heath-Brown has included themes like Conjecture, Distribution and Existential quantification in his Prime study.

In his study, Dirichlet eta function and Dirichlet kernel is inextricably linked to Generalized Dirichlet distribution, which falls within the broad field of Pure mathematics. His work carried out in the field of Calculus brings together such families of science as Prime-counting function, Analytic number theory and Riemann hypothesis, Geometric function theory. The various areas that he examines in his Prime zeta function study include Riemann Xi function and Explicit formulae.

- The Theory of the Riemann Zeta-Function (2277 citations)
- ARTIN'S CONJECTURE FOR PRIMITIVE ROOTS (239 citations)
- Zero-free regions for Dirichlet $L$-functions, and the least prime in an arithmetic progression (200 citations)

D. R. Heath-Brown focuses on Combinatorics, Discrete mathematics, Pure mathematics, Number theory and Prime. The study incorporates disciplines such as Quadratic equation and Type in addition to Combinatorics. D. R. Heath-Brown studied Discrete mathematics and ε-quadratic form that intersect with Isotropic quadratic form.

His Pure mathematics research is multidisciplinary, incorporating perspectives in Mathematical analysis and Quartic function. His research in Number theory intersects with topics in Exponential sum and Field. His Riemann hypothesis research is multidisciplinary, incorporating elements of Elliptic curve and Explicit formulae.

- Combinatorics (50.60%)
- Discrete mathematics (25.00%)
- Pure mathematics (23.21%)

- Pure mathematics (23.21%)
- Combinatorics (50.60%)
- Hasse principle (6.55%)

D. R. Heath-Brown mainly investigates Pure mathematics, Combinatorics, Hasse principle, Algebraic number field and Polynomial. His study looks at the relationship between Pure mathematics and topics such as Variety, which overlap with Hardy–Littlewood circle method, Degree and Dimension. In his study, D. R. Heath-Brown carries out multidisciplinary Combinatorics and Exponent research.

His study looks at the intersection of Hasse principle and topics like Complete intersection with Diophantine equation. His research on Algebraic number field also deals with topics like

- Intersection that connect with fields like Invertible matrix,
- Diophantine geometry which is related to area like Noncommutative geometry, Algebra and Modular form. His research integrates issues of Arbitrarily large, Type and Finite field in his study of Polynomial.

- Forms in many variables and differing degrees (20 citations)
- Simultaneous Integer Values of Pairs of Quadratic Forms (19 citations)
- RATIONAL POINTS ON INTERSECTIONS OF CUBIC AND QUADRIC HYPERSURFACES (16 citations)

- Algebra
- Number theory
- Mathematical analysis

Pure mathematics, Prime, Discrete mathematics, Combinatorics and Hasse principle are his primary areas of study. His study in the field of Quadric and Complete intersection is also linked to topics like Mean value theorem and Vinogradov. His Prime research includes themes of Asymptotic formula and Moduli.

His research in the fields of Sieve theory, Prime number and Perfect power overlaps with other disciplines such as Theory of Forms. His studies in Combinatorics integrate themes in fields like Quadratic equation, Class number, Class, Quadratic field and Pointwise. His Hasse principle study combines topics from a wide range of disciplines, such as Dimension, Degree, Conjecture, Variety and Hardy–Littlewood circle method.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

The Theory of the Riemann Zeta-Function

Edward Charles Titchmarsh;D. R. Heath-Brown.

**(1987)**

3948 Citations

The Theory of the Riemann Zeta-Function

Edward Charles Titchmarsh;D. R. Heath-Brown.

**(1987)**

3948 Citations

ARTIN'S CONJECTURE FOR PRIMITIVE ROOTS

D. R. Heath-Brown.

Quarterly Journal of Mathematics **(1986)**

386 Citations

ARTIN'S CONJECTURE FOR PRIMITIVE ROOTS

D. R. Heath-Brown.

Quarterly Journal of Mathematics **(1986)**

386 Citations

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

D. R. Heath-Brown.

Proceedings of The London Mathematical Society **(1992)**

308 Citations

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

D. R. Heath-Brown.

Proceedings of The London Mathematical Society **(1992)**

308 Citations

The density of rational points on curves and surfaces

D. R. Heath-Brown.

Annals of Mathematics **(2002)**

289 Citations

The density of rational points on curves and surfaces

D. R. Heath-Brown.

Annals of Mathematics **(2002)**

289 Citations

A mean value estimate for real character sums

D. R. Heath-Brown.

Acta Arithmetica **(1995)**

254 Citations

A mean value estimate for real character sums

D. R. Heath-Brown.

Acta Arithmetica **(1995)**

254 Citations

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