Relevant bibliographies by topics / Mahler measure / Dissertations / Theses
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Dissertations / Theses on the topic 'Mahler measure'

Author: Grafiati
Published: 4 June 2021
Last updated: 29 January 2023

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1

Rogers, Mathew D. "Hypergeometric functions and Mahler measure." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1420.

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The logarithmic Mahler measure of an n-variable Laurent polynomial, P(x1,...,xn) is defined by [expression]. Using experimental methods, David Boyd conjectured a large number of explicit relations between Mahler measures of polynomials and special values of different types of L-series. This thesis contains four papers which either prove or attempt to prove conjectures due to Boyd. The introductory chapter contains an overview of the contents of each manuscript.
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2

Staines, Matthew. "On the inverse problem for Mahler Measure." Thesis, University of East Anglia, 2012. https://ueaeprints.uea.ac.uk/48118/.

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We investigate a number of aspects of the inverse problem for Mahler Measure. If β is an algebraic unit, we demonstrate how to determine if there are any reciprocal numbers with measure β. We also give a formula for the number of integer polynomials with measure β and given degree.
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3

Chern, Shey-jey. "Estimates for the number of polynomials with bounded degree and bounded Mahler measure /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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4

De, Silva Dilum P. "Lind-Lehmer constant for groups of the form Z[superscript]n[subscript]p." Diss., Kansas State University, 2013. http://hdl.handle.net/2097/16244.

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5

Mohamed, Ismail Mohamed Ishak. "Lower bounds for heights in cyclotomic extensions and related problems." Diss., Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/2274.

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6

Mehrabdollahei, Mahya. "La mesure de Mahler d’une famille de polynômes exacts." Thesis, Sorbonne université, 2022. https://accesdistant.sorbonne-universite.fr/login?url=https://theses-intra.sorbonne-universite.fr/2022SORUS170.pdf.

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Dans cette thèse, nous étudions la suite de mesures de Mahler d’une famille de polynômes à deux variables exacts et réguliers, que nous notons Pd := P0≤i+j≤d xiyj . Elle n’est bornée ni en volume, ni en genre de la courbe algébrique sous-jacente. Nous obtenons une expression pour la mesure de Mahler de Pd comme somme finie de valeurs spéciales du dilogarithme de Bloch-Wigner. Nous utilisons SageMath pour approximer m(Pd) pour 1 ≤ d ≤ 1000. En recourant à trois méthodes différentes, nous prouvons que la limite de la suite de mesures de Mahler de cette famille converge vers 92π2 ζ(3). De plus, n
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7

Santos, Jefferson Marques. "Altura e equidistribuição de pontos algébricos." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/7564.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-07-05T14:04:12Z No. of bitstreams: 2 Dissertação - Jefferson Marques Santos - 2017.pdf: 1510253 bytes, checksum: fa6dbf92bac6614d3ce705a47bbe41b8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-07-10T14:31:22Z (GMT) No. of bitstreams: 2 Dissertação - Jefferson Marques Santos - 2017.pdf: 1510253 bytes, checksum: fa6dbf92bac6614d3ce705a47bbe41b8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>M
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8

Fhlathuin, Brid ni. "Mahler's measure on Abelian varieties." Thesis, University of East Anglia, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296951.

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This thesis is a study of the integration of proximity functions over certain compact groups. Mean values are found of the ultrametric valuation of certain rational functions associated with a divisor on an abelian variety, and it is shown how these may be expressed in terms of an integral, thus finding the analogue, for an abelian variety, of Mahler's definition of the measure of a polynomial. These integrals are shown to arise in a manner which mimics classical Riemann sums, and their relation with the global canonical height is investigated. It is shown that the measure is a rational multip
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9

Condon, John Donald. "Mahler measure evaluations in terms of polylogarithms." Thesis, 2004. http://hdl.handle.net/2152/1218.

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10

Condon, John Donald Rodríguez Villegas Fernando. "Mahler measure evaluations in terms of polylogarithms." 2004. http://wwwlib.umi.com/cr/utexas/fullcit?p3142710.

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11

Roy, Subham. "Generalized Mahler measure of a family of polynomials." Thèse, 2019. http://hdl.handle.net/1866/23797.

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Le présent mémoire traite une variation de la mesure de Mahler où l'intégrale de définition est réalisée sur un tore plus général. Notre travail est basé sur une famille de polynômes tempérée originellement étudiée par Boyd, P_k (x, y) = x + 1/x + y + 1/y + k avec k ∈ R_{>4}. Pour le k = 4 cas, nous utilisons des valeurs spéciales du dilogarithme de Bloch-Wigner pour obtenir la mesure de Mahler de P_4 sur un tore arbitraire (T_ {a, b})^2 = {(x, y) ∈ C* X C* : | x | = a, | y | = b } avec a, b ∈ R_{> 0}. Ensuite, nous établissons une relation entre la mesure de Mahler de P_8 sur un tore (T_ {a,
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12

Gu, Jarry. "Polylogarithmes et mesure de Mahler." Thesis, 2020. http://hdl.handle.net/1866/24344.

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Le but principal de ce mémoire est de calculer la mesure de Mahler logarithmique d’une famille de polynômes à trois variables x^n + 1 + (x^(n−1) + 1)y + (x − 1)z. Pour réaliser cet objectif, on intègre des régulateurs définis sur des complexes motiviques polylogarithmiques. Pour comprendre ces régulateurs, on explore les propriétés des polylogarithmes et démontre quelques identités polylogarithmiques. Ensuite, on utilise les régulateurs afin de simplifier l’intégrante. Notre résultat est une formule qui relie la mesure de Mahler de la famille de polynômes susmentionnée au dilogarithme de Bloch
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13

Lalín, Matilde Noemí Rodriguez-Villegas Fernando. "Some relations of Mahler measure with hyperbolic volumes and special values of L-functions." 2005. http://repositories.lib.utexas.edu/bitstream/handle/2152/1971/lalinm19850.pdf.

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14

Lalín, Matilde Noemí. "Some relations of Mahler measure with hyperbolic volumes and special values of L-functions." Thesis, 2005. http://hdl.handle.net/2152/1971.

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15

Miner, Zachary Layne. "Norms extremal with respect to the Mahler measure and a generalization of Dirichlet's unit theorem." Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-05-3197.

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In this thesis, we introduce and study several norms constructed to satisfy an extremal property with respect to the Mahler measure. These norms naturally generalize the metric Mahler measure introduced by Dubickas and Smyth. We show that bounding these norms on a certain subspace implies Lehmer's conjecture and in at least one case that the converse is true as well. We evaluate these norms on a class of algebraic numbers that include Pisot and Salem numbers, and for surds. We prove that the infimum in the construction is achieved in a certain finite dimensional space for all algebraic numbers
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16

Lechasseur, Jean-Sébastien. "Mesure de Mahler supérieure de certaines fonctions rationelles." Thèse, 2012. http://hdl.handle.net/1866/8989.

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Nous exprimons la mesure de Mahler 2-supérieure et 3-supérieure de certaines fonctions rationnelles en terme de valeurs spéciales de la fonction zêta, de fonctions L et de polylogarithmes multiples. Les résultats obtenus sont une généralisation de ceux obtenus dans [10] pour la mesure de Mahler classique. On améliore un de ces résultats en réduisant une combinaison linéaire de polylogarithmes multiples en termes de valeurs spéciales de fonctions L. On termine avec la réduction complète d’un cas particuler.<br>The 2-higher and 3-higher Mahler measure of some rational functions are given in term
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17

Fili, Paul Arthur. "Orthogonal decompositions of the space of algebraic numbers modulo torsion." Thesis, 2010. http://hdl.handle.net/2152/ETD-UT-2010-05-1416.

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We introduce decompositions determined by Galois field and degree of the space of algebraic numbers modulo torsion and the space of algebraic points on an elliptic curve over a number field. These decompositions are orthogonal with respect to the natural inner product associated to the L² Weil height recently introduced by Allcock and Vaaler in the case of algebraic numbers and the inner product naturally associated to the Néron-Tate canonical height on an elliptic curve. Using these decompositions, we then introduce vector space norms associated to the Mahler measure. For algebraic numbers,
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18

Giard, Antoine. "La mesure de Mahler d’une forme de Weierstrass." Thèse, 2019. http://hdl.handle.net/1866/22549.

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19

Issa, Zahraa. "A Generalization of a Theorem of Boyd and Lawton." Thèse, 2012. http://hdl.handle.net/1866/8745.

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Ce mémoire s’applique à étudier d’abord, dans la première partie, la mesure de Mahler des polynômes à une seule variable. Il commence en donnant des définitions et quelques résultats pertinents pour le calcul de telle hauteur. Il aborde aussi le sujet de la question de Lehmer, la conjecture la plus célèbre dans le domaine, donne quelques exemples et résultats ayant pour but de résoudre la question. Ensuite, il y a l’extension de la mesure de Mahler sur les polynômes à plusieurs variables, une démarche semblable au premier cas de la mesure de Mahler, et le sujet des points limites a
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