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q-Analogues of the (E.2) and (F.2) supercongruences of Van Hamme

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Abstract

Motivated by Zudilin’s work, we give q-analogues of the Ramanujan-type supercongruences (E.2) and (F.2) of Van Hamme. Our proof utilizes the q-WZ method and properties of cyclotomic polynomials. Using the same q-WZ pair, we also give q-analogues of some similar supercongruences due to He and Swisher. Additionally, we propose several related conjectures on supercongruences or q-supercongruences.

Keywords

Ramanujan Supercongruences q-Analogues Cyclotomic polynomials q-WZ pair 

Mathematics Subject Classification

Primary 11B65 Secondary 05A10 05A30 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesHuaiyin Normal UniversityHuai’anPeople’s Republic of China

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