Number theory with an emphasis on the Markoff spectrum / edited by Andrew Pollington, William Moran.

Format:

Book

Contributor:

Pollington, Andrew D., 1953-

Moran, W.

Series:

Lecture notes in pure and applied mathematics ; v. 147.

Lecture notes in pure and applied mathematics ; v. 147

Language:

English

Subjects (All):

Number theory--Congresses.

Number theory.

Markov spectrum--Congresses.

Markov spectrum.

Genre:

Conference papers and proceedings.

Physical Description:

viii, 321 pages : illustrations ; 26 cm.

Place of Publication:

New York : M. Dekker, 1993.

Summary:

Presenting the proceedings of a recently held conference in Provo, Utah, this essential reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum. Detailing the integration of geometric, algebraic, analytic, and arithmetic ideas, Number Theory with an Emphasis on the Markoff Spectrum contains refereed contributions on general problems of diophantine approximation ... quadratic forms and their connections with automorphic forms ... the modular group and its subgroups ... continued fractions ... hyperbolic geometry ... the lower part of the Markoff spectrum ... and more. Written by over 30 authorities in the field, Number Theory with an Emphasis on the Markoff Spectrum is a valuable resource for research mathematicians in harmonic analysis, number theory, algebra, geometry, and probability, and graduate students in these disciplines.

Contents:

The Hurwitz Equations / Arthur Baragar 1

Best Approximation of Real Numbers by Pisot Numbers / David W. Boyd 9

Some Metric Properties of Sum Sets / Gavin Brown, Qing-He Yin 17

Computing Endpoints in Markoff Spectra / Richard T. Bumby 23

Badly Approximable Systems and Inhomogeneous Approximation Over Number Fields / Edward B. Burger 33

U-Numbers and T-Numbers: Some Elementary Transcendence and Algebraic Independence Results / Deanna M. Caveny 43

The Arithmetic of Well-Approximated Numbers / Deanna Caveny, Robert Tubbs 53

Some Remarks on Triangular Numbers / Jasbir Chahal, Harry D'Souza 61

Markoff Geodesics in Matrix Theory / Harvey Cohn 69

Single Self-Intersection Geodesics and the Markoff Spectrum / David J. Crisp, William Moran 83

An Inhomogeneous Hall's Ray / T. W. Cusick, W. Moran, A. D. Pollington 95

An Exponential Sum Over Primes / D. A. Goldston 101

Geometric Markoff Theory and a Theorem of Millington / Andrew Haas 107

On the Fourier Coefficients of the Modular Invariant (j - 12[superscript 3])[superscript 1/2] / Joseph Lehner 113

On Zeta Functions Associated to the Product of Two Eisenstein Series / Bradford F. Lyon 131

A Sampler of Recent Developments in the Distribution of Sequences / G. Myerson 163

The Simplest Inverse Problems in Additive Number Theory / Melvyn B. Nathanson 191

Sum Sets and U-Numbers / Andrew D. Pollington 207

Ergodic Theory of Complex Continued Fractions / Asmus L. Schmidt 215

Remarks on the Rosen [lambda]-Continued Fractions / Thomas A. Schmidt 227

Continued Fractions and Congruence Subgroup Geodesics / Mark Sheingorn 239

The Tensor Emptiness of Certain Lattice Subsets Arising from the Hardy-Littlewood Circle Method / Brent Smith 255

Refinements of the Erdos-Turan Inequality / Jeffrey D. Vaaler 263

Schneider's Continued Fraction / A. J. van der Poorten 271

On the Eigenvalues of Redheffer's Matrix, I / R. C. Vaughan 283

Maximal Fuchsian Subgroups of Extended Bianchi Groups / L. Ya. Vulakh 297

On Cuspidal Eigenforms Constructed from Theta Series / Lynne H. Walling 311

A Note on Symmetric Diagonal Equations / Trevor D. Wooley 317.

Notes:

Includes bibliographical references.

ISBN:

0824789024

OCLC:

27336459