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pro vyhledávání: '"GRIZZARD, Robert"'
Autor:
Grizzard, Robert
We draw connections between the various conjectures which are included in G. R\'emond's generalized Lehmer problems. Specifically, we show that the degree one form of his conjecture for the multiplicative group is, in a sense, almost as strong as the
Externí odkaz:
http://arxiv.org/abs/1710.11614
Autor:
Grizzard, Robert, Vaaler, Jeffrey D.
Let $K/\mathbb{Q}$ be an algebraic extension of fields, and let $\alpha \not= 0$ be contained in an algebraic closure of $K$. If $\alpha$ can be approximated by roots of numbers in $K^{\times}$ with respect to the Weil height, we prove that some nonz
Externí odkaz:
http://arxiv.org/abs/1710.08399
Autor:
Grizzard, Robert Vernon Lees
This dissertation contains a number of results on properties of infinite algebraic extensions of the rational field, all of which have a view toward the study of heights in diophantine geometry. We investigate whether subextensions of extensions gene
Externí odkaz:
http://hdl.handle.net/2152/24822
Autor:
Grizzard, Robert, Gunther, Joseph
Publikováno v:
Alg. Number Th. 11 (2017) 1385-1436
Masser and Vaaler have given an asymptotic formula for the number of algebraic numbers of given degree $d$ and increasing height. This problem was solved by counting lattice points (which correspond to minimal polynomials over $\mathbb{Z}$) in a homo
Externí odkaz:
http://arxiv.org/abs/1609.08720
Publikováno v:
Int. Math. Res. Notices (2015) 2015 (20): 10657-10679
Let $F$ be an algebraic extension of the rational numbers and $E$ an elliptic curve defined over some number field contained in $F$. The absolute logarithmic Weil height, respectively the N\'eron-Tate height, induces a norm on $F^*$ modulo torsion, r
Externí odkaz:
http://arxiv.org/abs/1408.4915
Autor:
Grizzard, Robert
Publikováno v:
Acta Arithmetica 170 (2015) , 1-13
An algebraic extension K of the rationals has the Bogomolov property if the absolute logarithmic height of non-torsion points of K* is bounded away from 0. We define a relative extension L/K to be Bogomolov if this holds for points of L\K. We constru
Externí odkaz:
http://arxiv.org/abs/1309.2998
Publikováno v:
Ramanujan J. 35 (2014), no. 2, 327-338
Bruinier and Ono recently developed the theory of generalized Borcherds products, which uses coefficients of certain Maass forms as exponents in infinite product expansions of meromorphic modular forms. Using this, one can use classical results on co
Externí odkaz:
http://arxiv.org/abs/1308.3454
Autor:
Gal, Itamar, Grizzard, Robert
Publikováno v:
J. Th\'eor. Nombres Bordeaux 26 (2014) no. 3, 655-672
Let k be a number field, and denote by k^[d] the compositum of all degree d extensions of k in a fixed algebraic closure. We first consider the question of whether all algebraic extensions of k of degree less than d lie in k^[d]. We show that this oc
Externí odkaz:
http://arxiv.org/abs/1210.4217
Autor:
GAL, Itamar, GRIZZARD, Robert
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2014 Jan 01. 26(3), 655-672.
Externí odkaz:
https://www.jstor.org/stable/43973207
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