What is he best known for?
The fields of study he is best known for:
- 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.
His most cited work include:
- 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)
What are the main themes of his work throughout his whole career to date?
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.
He most often published in these fields:
- Combinatorics (50.60%)
- Discrete mathematics (25.00%)
- Pure mathematics (23.21%)
What were the highlights of his more recent work (between 2014-2020)?
- Pure mathematics (23.21%)
- Combinatorics (50.60%)
- Hasse principle (6.55%)
In recent papers he was focusing on the following fields of study:
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.
Between 2014 and 2020, his most popular works were:
- 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)
In his most recent research, the most cited papers focused on:
- 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.
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