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Christopher Hooley. 7 August 1928—13 December 2018

Autor: D. R. Heath-Brown

Publikováno v: Biographical Memoirs of Fellows of the Royal Society. 69:225-246

Christopher Hooley was one of the leading analytic number theorists of his day, world-wide. His early work on Artin’s conjecture for primitive roots remains the definitive investigation in the area. His greatest contribution, however, was the intro

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d0183637acea2a84d05401ed7b915b56
https://doi.org/10.1098/rsbm.2020.0027

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Irreducible polynomials over finite fields produced by composition of quadratics

Autor: Giacomo Micheli, D. R. Heath-Brown

Publikováno v: Revista Matemática Iberoamericana. 35:847-855

For a set $S$ of quadratic polynomials over a finite field, let $C$ be the (infinite) set of arbitrary compositions of elements in $S$. In this paper we show that there are examples with arbitrarily large $S$ such that every polynomial in $C$ is irre

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https://doi.org/10.4171/rmi/1072

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Density of rational points on a quadric bundle in P 3 × P 3

Autor: Tim D Browning, D. R. Heath-Brown

Publikováno v: Duke Mathematical Journal. 169

We establish an asymptotic formula for the number of rational points of bounded anticanonical height which lie on a certain Zariski-dense subset of the biprojective hypersurface x 1 y 2 1 + ⋯ + x 4 y 2 4 = 0 in P 3 × P 3 . This confirms the modifi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::45aa0e5253bc49f1f06254cec707b1a3
https://doi.org/10.1215/00127094-2020-0031

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CHRISTOPHER HOOLEY - BIBLIOGRAPHY from CHRISTOPHER HOOLEY. 7 August 1928—;13 December 2018

Autor: D. R. Heath-Brown

Christopher Hooley was one of the leading analytic number theorists of his day, world-wide. His early work on Artin's conjecture for primitive roots remains the definitive investigation in the area. His greatest contribution, however, was the introdu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7521a5500ede9fb2ecf9ccc7f2dc2f1a

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Rational points on the intersection of three quadrics

Autor: D. R. Heath-Brown

Publikováno v: International Journal of Number Theory. 13:273-289

We prove the Hasse principle and weak approximation for varieties defined by the smooth complete intersection of three quadratics in at least 19 variables, over arbitrary number fields.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b92ff75b4e54ab2b081ee63fc3bc03f
https://doi.org/10.1142/s1793042117500178

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Forms in many variables and differing degrees

Autor: D. R. Heath-Brown, Tim D Browning

Publikováno v: Browning, T & Heath-Brown, R 2017, ' Forms in many variables and differing degrees ', Journal of the European Mathematical Society, vol. 19, no. 2, pp. 357-394 . https://doi.org/10.4171/JEMS/668

We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and

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https://doi.org/10.4171/jems/668

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Prime values of $$a^2 + p^4$$ a 2 + p 4

Autor: Xiannan Li, D. R. Heath-Brown

Publikováno v: Inventiones mathematicae. 208:441-499

We prove an asymptotic formula for the number of primes of the shape $$a^2+p^4$$ , thereby refining the well known work of Friedlander and Iwaniec (Ann Math (2) 148(3):945–1040, 1998). Along the way, we prove a result on equidistribution of primes

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https://doi.org/10.1007/s00222-016-0694-0

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Komaravolu Chandrasekharan (1920–2017)

Autor: D. R. Heath-Brown

Publikováno v: Acta Arithmetica. 185(2)

Komaravolu Chandrasekharan was born on November 21, 1920, in Machilipatnam, India. He obtained his M.A. in Mathematics from the University of Madras through Presidency College in 1943 and his Ph.D in 1946. He was a student of Ananda Rau, who worked w

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http://ora.ox.ac.uk/objects/uuid:

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The Differences Between Consecutive Smooth Numbers

Autor: D. R. Heath-Brown

We show that large gaps between smooth numbers are infrequent. The key new tool is a novel mean value bound for a special type of Dirichlet polynomial.
Comment: To appear in Acta Arithmetica

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