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NONOSCILLATION OF ELLIPTIC INTEGRALS RELATED TO CUBIC POLYNOMIALS WITH SYMMETRY OF ORDER THREE

Published online by Cambridge University Press:  01 May 1998

LUBOMIR GAVRILOV
LUBOMIR GAVRILOV
Affiliation:
Laboratoire Emile Picard, CNRS UMR 5580, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France
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Abstract

We study zeros of elliptic integrals I(h)=∫∫H[les ]hR(x, y)dx dy, where H(x, y) is a real cubic polynomial with a symmetry of order three, and R(x, y) is a real polynomial of degree at most n. It turns out that the vector space [Ascr ]n formed by such integrals is a Chebishev system: the number of zeros of each elliptic integral I(h)∈[Ascr ]n is less than the dimension of the vector space [Ascr ]n.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 30 , Issue 3 , May 1998 , pp. 267 - 273
Copyright
© The London Mathematical Society 1998

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