A supercongruence fantasy on Fibonacci and Lucas (after Guillera)
Wadim Zudilin
TL;DR
This paper explores advanced supercongruences involving Fibonacci, Lucas, and Apéry numbers, extending Ramanujan-type results and revealing new mathematical relationships inspired by Guillera's observations.
Contribution
It generalizes Ramanujan-type supercongruences to include Fibonacci, Lucas, and Apéry sequences, providing a broader framework for supercongruence phenomena.
Findings
Extended supercongruences for Fibonacci and Lucas sequences
Unified treatment of various special sequences in supercongruences
New mathematical identities inspired by Guillera's observations
Abstract
Motivated by observations of Guillera we generalise the so-called Ramanujan-type supercongruences to a further level in which the sequences of Fibonacci, Lucas, Ap\'ery numbers and their friends all receive a natural appearance.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Identities · Analytic Number Theory Research