Sums of three squares of fractions of two variables

DOI10.1007/s00229-004-0535-0zbMath1118.11020OpenAlexW1603254347MaRDI QIDQ1777263

Olivier Macé, Louis Mahé

Publication date: 13 May 2005

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-004-0535-0

zbMATH Keywords

sums of squaresdivisorrational functionselliptic curvePythagoras numberJacobian variety

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) (12D15) Elliptic curves (14H52) Forms over real fields (11E10)

Related Items (1)

Hilbert's Seventeenth Problem and Hyperelliptic Curves

Cites Work

• Positive definite rational functions of two variables which are not the sum of three squares
• On sums of squares and on elliptic curves over function fields
• Zur Darstellung definiter Funktionen als Summe von Quadraten. (To the representation of definite functions as the sum of squares)
• Geometrical aspects of the level of curves.
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