A Birch-Goldbach theorem

DOI10.1007/s00013-009-0086-4zbMath1241.11039OpenAlexW1982007310MaRDI QIDQ849218

Liu, Jianya, Jörg Brüdern, Trevor D. Wooley, Rainer Dietmann

Publication date: 25 February 2010

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-009-0086-4

zbMATH Keywords

prime numbersDiophantine equations

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Goldbach-type theorems; other additive questions involving primes (11P32) Diophantine equations in many variables (11D72)

Related Items (9)

Rational lines on cubic hypersurfaces ⋮ On forms in prime variables ⋮ Integral points on quadrics with prime coordinates ⋮ Diophantine equations in the primes ⋮ John Pell’s mathematical papers and the Royal Society’sEnglish Atlas, 1678–82 ⋮ PRIME SOLUTIONS TO POLYNOMIAL EQUATIONS IN MANY VARIABLES AND DIFFERING DEGREES ⋮ Rational linear spaces on hypersurfaces over quasi-algebraically closed fields ⋮ Finite Saturation for Unirational Varieties ⋮ Almost prime solutions to diophantine systems of high rank

Cites Work

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• The density of integer points on homogeneous varieties
• The primes contain arbitrarily long arithmetic progressions
• Sieving and expanders
• Small prime solutions of quadratic equations II
• Homogeneous forms of odd degree in a large number of variables
• Forms in many variables
• Small solutions of cubic equations with prime variables in arithmetic progressions
• Systems of cubic forms
• An explicit version of Birch's Theorem
• Linear Spaces on Cubic Hypersurfaces, and Pairs of Homogeneous Cubic Equations

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