Number Theory with an Emphasis on the Markoff Spectrum  book cover
1st Edition

Number Theory with an Emphasis on the Markoff Spectrum

ISBN 9780824789022
Published April 28, 1993 by CRC Press
352 Pages

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Book Description

Presenting the proceedings of a recently held conference in Provo, Utah, this 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; and the lower part of the Markoff spectrum.;Written by over 30 authorities in the field, this book should be a useful resource for research mathematicians in harmonic analysis, number theory algebra, geometry and probability and graduate students in these disciplines.

Table of Contents

The Hurwitz equations, Arthur Baragar; best approximation of real numbers by pisot numbers, David W. Boyd; some metric properties of sum sets, Gavin Brown and Qing-He Yin; computing endpoints in Markoff spectra, Richard T. Burnby; badly approximable systems and inhomogeneous approximation over number fields, Edward B. Burger; u-numbers and t-numbers - some elementary transcendence and algebraic independence results, Deanna M. Caveny; the arithmetic of well-approximated numbers, Deanna Caveny and Robert Tubbs; some remarks on triangular numbers, Jasbir Chahal and Harry D'Souza; Markoff geodesics in matrix theory, Harvey Cohn; single self-intersection geodesics and the Markoff spectrum, David J. Crisp and William Moran; an inhomogeneous hall's ray, T.W. Cusick, et al; an exponential sum over primes, D.A. Goldston; geometric Markoff theory and a theorem of millington, Andrew Haas; on the fourier coefficients of the modular invariant, (j-12 1/2)3, Joseph Lehner; on zeta functions associated to the product of two Eisenstein series, Bradford F. Lyon; a sampler of recent developments in the distribution of sequences, G. Myerson; the simplest inverse problems in additive number theory, Melvyn B. Nathanson; sum sets and u-numbers, Andrew D. Pollington; ergodic theory of complex continued fractions, Asmus L. Schmidt; remarks on the rosen l-continued fractions, Thomas A. Schmidt; continued fractions and congruence subgroup geodesics, Mark Sheingorn; the tensor emptiness of certain lattice subsets arising from the Hardy-Littlewood circle methods, Brent Smith; refinements of the Erdos-Turan inequality, Jeffrey D. Vaaler; Schneider's continued fraction, A.J. van der Poorten; on the eigenvalues of Redheffer's matrix I, R.C. Vaughan; maximal fuchsian subgroups of extended bianchi groups, L. Ya Vulakh; on cuspidal eigenforms constructed from theta series, Lynne H. Walling; a note on symmetric diagnosal equations, Trevor D. Wooley.

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