Metric Mahler measures over number fields
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DOI: 10.1007/s10474-017-0770-y
Abstract: For an algebraic number α, the metric Mahler measure $${m_1(\alpha)}$$m1(α) was first studied by Dubickas and Smyth [4] and was later generalized to the t-metric Mahler measure $${m_t(\alpha)}$$mt(α) by the author [16]. The definition of… read more here.
Keywords: metric mahler; number fields; mahler measures; number ... See more keywords
Mahler measures of elliptic modular surfaces
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DOI: 10.1090/tran/7524
Abstract: In this article we develop a new method for relating Mahler measures of three-variable polynomials that define elliptic modular surfaces to L-values of modular forms. Using an idea of Deninger, we express the Mahler measure… read more here.
Keywords: mahler measures; measures elliptic; modular surfaces; mahler ... See more keywords
Mahler measures, elliptic curves, and L-functions for the free energy of the Ising model.
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DOI: 10.1103/physreve.110.054134
Abstract: This work establishes links between the Ising model and elliptic curves via Mahler measures. First, we reformulate the partition function of the Ising model on the square, triangular, and honeycomb lattices in terms of the… read more here.
Keywords: mahler measures; ising model; free energy; elliptic curves ... See more keywords
Small Mahler measures with bounds on the house and shortness
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DOI: 10.4153/s0008439524000900
Abstract: Abstract We show that for any $\varepsilon>0$ , the number of monic, reciprocal, length- $5$ integer polynomials that have house at least $1+\varepsilon $ is finite. The proof is algorithmic, and we are consequently able… read more here.
Keywords: mahler measures; house least; polynomials house; mahler ... See more keywords