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

• DOI: 10.1007/s00209-013-1238-6
• Publication Date: 2013-10-28T11:57:53Z
• Authors: Matthew A. Papani...; Mathew D. Rogers; Detchat Samart
• Keywords: Calabi–Yau manifold; Laurent polynomial

11 pages<br/>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 S_4(Gamma_0(8)) and a Riemann zeta value. This is equivalent to a new formula for a 6F5-hypergeometric series evaluated at 1.<br/>