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Nonoscillation of Elliptic Integrals Related to Cubic Polynomials with Symmetry of Order Three
Author(s) -
Gavrilov Lubomir
Publication year - 1998
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609397004244
Subject(s) - mathematics , dimension (graph theory) , order (exchange) , symmetry (geometry) , polynomial , elliptic integral , degree (music) , space (punctuation) , mathematics subject classification , pure mathematics , quarter period , mathematical analysis , elliptic curve , geometry , physics , finance , economics , linguistics , philosophy , acoustics
We study zeros of elliptic integrals I ( h )=∫∫ H ⩽ h R ( x , y ) dxdy , 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 A n formed by such integrals is a Chebishev system: the number of zeros of each elliptic integral I ( h )∈A n is less than the dimension of the vector space A n . 1991 Mathematics Subject Classification 34C10.