Number Theory with an Emphasis on the Markoff Spectrum

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Andrew Pollington, William Moran
CRC Press, Apr 28, 1993 - Mathematics - 352 pages
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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.
 

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Contents

Best Approximation of Real Numbers by Pisot Numbers
9
Computing Endpoints in Markoff Spectra
23
Some Elementary Transcendence
43
Some Remarks on Triangular Numbers
61
Harvey Cohn
83
An Exponential Sum Over Primes
101
Joseph Lehner
131
A Sampler of Recent Developments in the Distribution of Sequences
163
The Simplest Inverse Problems in Additive Number Theory
191
Melvyn B Nathanson
207
Remarks on the Rosen XContinued Fractions
227
Mark Sheingorn
255
Schneiders Continued Fraction
271
Vaughan
297
Ya Vulakh
310
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