Doctor of Philosophy (PhD)
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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Bakhova, Maiia J., "A numerical investigation of Apéry-like recursions and related Picard-Fuchs equations" (2012). LSU Doctoral Dissertations. 729.