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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(Γ0(8)) and a Riemann zeta value. This is equivalent to a new formula for a 6F5-hypergeometric(More)
We prove that the (logarithmic) Mahler measure m(P ) of P (x, y) = x + 1/x + y + 1/y + 3 is equal to the L-value 2L′(E, 0) attached to the elliptic curve E : P (x, y) = 0 of conductor 21. In order to do this we investigate the measure of a more general Laurent polynomial Pa,b,c(x, y) = a ( x + 1 x ) + b ( y + 1 y ) + c and show that the wanted quantity m(P(More)
We give a brief introduction to Kronecker’s Jugendtraum, sometimes called Hilbert’s twelfth problem, which concerns ways to describe abelian extensions of arbitrary number field K using special values of transcendental functions. Only partial results have been proved and the general case still remains open until now. Specifically, we will explain how the(More)
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