A numerical investigation of Apéry-like recursions and related Picard-Fuchs equations

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.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2012

Author dc:creator

• Bakhova, Maiia J.

• Picard-Fuchs equations
• numerical investigation of recursions
• Verrill
• Zagier
• Apery

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-01312012-141528
https://repository.lsu.edu/gradschool_dissertations/729

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-1728