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Arithmetic upon an algebraic surface

1945/01/01 by Beniamino Segre · 1 citation
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #History and Theory of Mathematics #Polynomial and algebraic computation #Arithmetic function #Mathematics #Algebraic surface #Algebraic geometry #Algebraic number #Diophantine equation #Diophantine geometry #Surface (topology) #Algebraic curve #Algebraic function #Space (punctuation) #Quartic function #Algebra over a field #Pure mathematics #Arithmetic #Discrete mathematics #Geometry #Mathematical analysis #Computer science

paper · pdf · doi:10.1090/s0002-9904-1945-08300-1

openalex publication_date 1945/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07

Abstract

On a parametric solution of the equation x?-\-y z -\-az z =b, and on ternary forms representing every rational number, ibid. p. 31; On ternary nonhomogeneous cubic equations with more than one rational solution, ibid, p. 88; A parametric solution of the indeterminate cubic equation z 2 ~f(x, y), ibid. p. 226; A complete parametric solution of certain homogeneous Diophantine equations, of degree n in w+1 variables, ibid. vol. 19 (1944) p. 46. Another paper of mine, On arithmetical properties of singular cubic surfaces, will appear shortly in the same journal.

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