A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

##
###
Complete hyperelliptic integrals of the first kind and their non-oscillation

2003
*
Transactions of the American Mathematical Society
*

Let P (x) be a real polynomial of degree 2g + 1, H = y 2 + P (x) and δ(h) be an oval contained in the level set {H = h}. We study complete Abelian integrals of the form where α i are real and Σ ⊂ R is a maximal open interval on which a continuous family of ovals {δ(h)} exists. We show that the g-dimensional real vector space of these integrals is not Chebyshev in general: for any g > 1, there are hyperelliptic Hamiltonians H and continuous families of ovals δ(h) ⊂ {H = h}, h ∈ Σ, such that the

doi:10.1090/s0002-9947-03-03432-9
fatcat:dahelehqhjdndmuf6nrw7pug6u