Mahler measure of some -variable polynomial families
✍ Scribed by Matilde N. Lalín
- Book ID
- 104024576
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 324 KB
- Volume
- 116
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
The Mahler measures of some n-variable polynomial families are given in terms of special values of the Riemann zeta function and a Dirichlet L-series, generalizing the results of Lalín (J. Number Theory 103 (2003) 85-108). The technique introduced in this work also motivates certain identities among Bernoulli numbers and symmetric functions.
📜 SIMILAR VOLUMES
This paper is concerned with the study of Mahler's measure of an univariate polynomial. A theorem of Szego says that the measure of P is equal to the infimum of &PQ& 2 where Q is a monic polynomial. Here we study how the infimum of &PQ& 2 , where Q is monic and has degree k, tends to the measure of
We prove several identities relating three-variable Mahler measures to integrals of inverse trigonometric functions. After deriving closed forms for most of these integrals, we obtain ten explicit formulas for threevariable Mahler measures. Several of these results generalize formulas due to Condon