The Mahler measure of a Calabi-Yau threefold and special -values

abstract

• The aim of this paper is to prove a Mahler measure formula of a four-variable Laurent polynomial whose zero locus defines a Calabi-Yau threefold. We show that its Mahler measure is a rational linear combination of a special L-value of the normalized newform in S4(0(8)) and a Riemann zeta value. This is equivalent to a new formula for a 6F5-hypergeometric series evaluated at 1. 2013 Springer-Verlag Berlin Heidelberg.

authors

• Papanikolas, Matthew

published proceedings

• MATHEMATISCHE ZEITSCHRIFT

author list (cited authors)

• Papanikolas, M. A., Rogers, M. D., & Samart, D.

citation count

• 4

complete list of authors

• Papanikolas, Matthew A||Rogers, Mathew D||Samart, Detchat

publication date

• April 2014

publisher

• Springer Nature  Publisher

published in

• Mathematische Zeitschrift  Journal

keywords

• Calabi-yau Threefold
• Elliptic Integrals
• Hypergeometric Series
• Mahler Measure
• Modular Form

Digital Object Identifier (DOI)

• 10.1007/s00209-013-1238-6

start page

• 1151

end page

• 1163

volume

• 276

issue

• 3-4

URL

• http://dx.doi.org/10.1007/s00209-013-1238-6