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The Mahler measure of a Calabi-Yau threefold and special L-values (1305.2143v1)
Published 9 May 2013 in math.NT
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 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.