3F2-hypergeometric functions and supersingular elliptic curves

Pitman, Sarah

doi:10.2140/involve.2015.8.481

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ISSN (electronic): 1944-4184

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${}_3 F_2$-hypergeometric functions and supersingular elliptic curves

Sarah Pitman

Vol. 8 (2015), No. 3, 481–490

DOI: 10.2140/involve.2015.8.481

Abstract

In recent work, Monks described the supersingular locus of families of elliptic curves in terms of $_{2} F_{1}$ -hypergeometric functions. We lift his work to the level of $_{3} F_{2}$ -hypergeometric functions by means of classical transformation laws and a theorem of Clausen.

Keywords

hypergeometric functions, supersingular, elliptic curves

Mathematical Subject Classification 2010

Primary: 11G20, 33C20

Milestones

Received: 17 July 2013

Revised: 2 September 2013

Accepted: 4 September 2013

Published: 5 June 2015

Communicated by Ken Ono

Authors

Sarah Pitman
Emory University Department of Mathematics and Computer Science 400 Dowman Drive Atlanta, Georgia 30322 United States

Vol. 8, No. 3, 2015