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Number Theory and Discrete Mathematics pp 225–230Cite as

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Hilbert’s Seventeenth Problem and Pfister’s Work on Quadratic Forms

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Abstract

On August 8, 1900, David Hilbert [5], in his famous address at the International Congress of Mathematicians in Paris, proposed twenty three problems as sign posts for twentieth century Mathematics; the seventeenth being

Hilbert‘s Conjecture. A Ncessary and sufficient condition that f(X 1,X 2,…,X n)∈ ℝ(X 1,X 2,…,X n) is a sum of squares (sos) in ℝ(X 1,X 2,…,X n) is that f (X 1,X 2,…,X n) is, positive semi definite (psd),i.e. f(X 1,X 2,…,X n)≥ 0 for all a 1,a,2,…,a n ∈ ℝ for which f is defined.

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Authors and Affiliations

  1. Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India

    A. R. Rajwade

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  1. A. R. Rajwade
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Editors and Affiliations

  1. Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, 160014, India

    A. K. Agarwal

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© 2002 Springer Basel AG

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Rajwade, A.R. (2002). Hilbert’s Seventeenth Problem and Pfister’s Work on Quadratic Forms. In: Agarwal, A.K., Berndt, B.C., Krattenthaler, C.F., Mullen, G.L., Ramachandra, K., Waldschmidt, M. (eds) Number Theory and Discrete Mathematics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8223-1_22

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  • DOI: https://doi.org/10.1007/978-3-0348-8223-1_22

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9481-4

  • Online ISBN: 978-3-0348-8223-1

  • eBook Packages: Springer Book Archive

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