Title page for ETD etd-01312012-141528


Type of Document Dissertation
Author Bakhova, Maiia J.
Author's Email Address mayab@math.lsu.edu
URN etd-01312012-141528
Title A Numerical Investigation of Apery-like Equations and Related Picard-Fuchs Equations
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Perlis, Robert Committee Chair
Adkins, William Committee Member
Gilmer, Patrick Committee Member
He, Hongyu Committee Member
Wu, Hsiao-Chun Dean's Representative
Keywords
  • Picard-Fuchs equations
  • numerical investigation of recursions
  • Verrill
  • Zagier
  • Apery
Date of Defense 2011-12-02
Availability unrestricted
Abstract
In this work we investigate a generalization of a recursion which was used by Apery in his proof of irrationality of the zeta function values at 2 and 3. It is a continuation of the work of Zagier , who considered generalization of the first equation and numerically investigated it. The study is made for two generalizations of the second equation, one used the mirror symmetry idea from the theory of Calabi-Yau varieties and another worked with recursion. There were discovered connections between them.
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