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arXiv · 1503.06069

Mahler measures, K-theory and values of L-functions

Hubert Bornhorn
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Abstract

The Mahler measure of a polynomial $P$ in $n$ variables is defined as the mean of $\log|P|$ over the $n$-dimensional torus. For certain polynomials with integer coefficients in two variables the Mahler measure is known to be related to special values of L-functions of arithmetic objects (e.g. Dirichlet characters and elliptic curves over $\mathbb{Q}$). Inspired by work of Deninger Boyd has investigated this relationship numerically. In this paper we reduce some conjectures of Boyd to Beilinson`s conjectures on special values of L-functions. The methods in use are widely of K-theoretical nature.

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Hubert Bornhorn. 2015-03-20. Mahler measures, K-theory and values of L-functions. https://arxiv.org/abs/1503.06069

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