Search Results - "Vaaler, Jeffrey D."

Counting algebraic numbers with large height II by Masser, David, Vaaler, Jeffrey D.

“…We count algebraic numbers of fixed degree over a fixed algebraic number field. When the heights of the algebraic numbers are bounded above by a large…”
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Gaussian subordination for the Beurling-Selberg extremal problem by CARNEIRO, EMANUEL, LITTMANN, FRIEDRICH, VAALER, JEFFREY D.

“…<<. Further applications to number theory include optimal approximations of theta functions by trigonometric polynomials and optimal bounds for certain…”
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Heights on groups and small multiplicative dependencies by VAALER, JEFFREY D.

“… The height of a finitely generated subgroup is shown to equal the volume of a certain naturally occurring, convex, symmetric subset of Euclidean space. This…”
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SOME EXTREMAL FUNCTIONS IN FOURIER ANALYSIS. II by CARNEIRO, EMANUEL, VAALER, JEFFREY D.

“…We obtain extremal majorants and minorants of exponential type for a class of even functions on ${\Bbb R}$ which includes log|x| and |x|α, where -1 < α < 1. We…”
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Sums of products of fractional parts by Hoàng Lê, Thái, Vaaler, Jeffrey D.

“…We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special…”
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Minkowski’s theorem on independent conjugate units by Akhtari, Shabnam, Vaaler, Jeffrey D.

“…We call a unit β in a finite Galois extension l / Q a Minkowski unit if the subgroup generated by β and its conjugates over Q has maximum rank in the unit…”
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Generalizations of Gonçalves' inequality by Borwein, Peter, Mossinghoff, Michael J., Vaaler, Jeffrey D.

“…Let F(z)=\sum_{n=0}^N a_n z^n be a polynomial with complex coefficients and roots \alpha_1, \ldots, \alpha_N, let \|F\|_p denote its L_p norm over the unit…”
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Multiplicatively badly approximable matrices in fields of power series by Lê, Thái Hoàng, Vaaler, Jeffrey D.

“…We study the notion of multiplicatively badly approximable matrices in the field of a Laurent series with coefficients in a field K. We prove a transference…”
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Lower bounds for regulators of number fields in terms of their discriminants by AKHTARI, Shabnam, VAALER, Jeffrey D.

“…Nous prouvons une inégalité qui compare le régulateur d’un corps de nombres et la valeur absolue de son discriminant. Nous affinons les idées de Silverman [15]…”
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Note on a Diophantine inequality in several variables by Barton, Jeffrey T., Montgomery, Hugh L., Vaaler, Jeffrey D.

“…We establish estimates for the number of points that belong to an aligned box in (\mathbb{R}/\mathbb{Z})^N in terms of certain exponential sums. These…”
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Some Extremal Functions in Fourier Analysis, III by Carneiro, Emanuel, Vaaler, Jeffrey D.

“…We obtain the best approximation in L 1 (ℝ), by entire functions of exponential type, for a class of even functions that includes e − λ | x | , where λ >0, log…”
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The Least Nonsplit Prime in Galois Extensions of Q by Vaaler, Jeffrey D, Voloch, José Felipe

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Perturbing polynomials with all their roots on the unit circle by Mossinghoff, Michael J., Pinner, Christopher G., Vaaler, Jeffrey D.

“…Given a monic real polynomial with all its roots on the unit circle, we ask to what extent one can perturb its middle coefficient and still have a polynomial…”
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On the number of lattice points in a ball by Vaaler, Jeffrey D

“…Communications in Mathematics, Volume 31 (2023), Issue 2 (Special issue: Euclidean lattices: theory and applications) (June 5, 2023) cm:11119 We prove a fairly…”
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An ABC inequality for Mahler’s measure by Vaaler, Jeffrey D.

“… We prove an upper bound for the Mahler measure of the Wronskian of a collection of N linearly independent polynomials with complex coefficients. If the…”
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Lower Bounds for Regulators of Number Fields in terms of their Discriminants by Akhtari, Shabnam, Vaaler, Jeffrey D

“…We prove inequalities that compare the regulator of a number field with its absolute discriminant. We refine some ideas in Silverman's work in 1984 where such…”
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Reviews by Nunemacher, Jeffrey, Vaaler, Jeffrey D.

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Reviews by Nunemacher, Jeffrey, Vaaler, Jeffrey D.

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A bound for the exterior product of $S$-units by Akhtari, Shabnam, Vaaler, Jeffrey D

“…We generalize an inequality for the determinant of a real matrix proved by A. Schinzel, to more general exterior products of vectors in Euclidean space. We…”
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A geometric inequality with applications to linear forms by Vaaler, Jeffrey

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