International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 41-48
doi:10.1155/S0161171293000043
On the monotonicity of the quotient of certain abelian integrals
Department of Mathematics, University of Northern Iowa, Cedar Falls 50614, Iowa, USA
Received 6 September 1991; Revised 17 October 1991
Copyright © 1993 Min Ho Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We prove that the quotient of abelian integrals associated to an elliptic surface
is bounded and strictly increasing by first determining the Picard-Fuchs equation satisfied by the
abelian integrals and the Riccati equation satisfied by the quotient of the abelian integrals.