## Number Theory with an Emphasis on the Markoff SpectrumPresenting 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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 |

### Common terms and phrases

ak-i algebraic independence algebraic numbers algorithm apply arithmetic automorphism Bianchi group closed geodesies Cohn complex numbers compute congruences conjugacy class consider constant continued fraction expansion converges COROLLARY corresponding cusp Dedekind sums define denote Diophantine approximation divisor eigenforms eigenvalues Eisenstein series elements equation Ergodic Farey sets fixed follows Fourier coefficients Fuchsian groups Fuchsian subgroup function generalixation geodesic geometry given Hence Hermitian form hyperbolic inequality infinite interval Lemma lower bound Markoff forms Markoff spectrum Math matrix measure modular forms modular group modulo node non-xero number theory obtain orbifold partial quotients Pell's equation periodic Pisot polynomial positive integer prime problem proof of Theorem prove punctured quadratic forms rational real number result Riemann satisfy set of integers Sheingorn step-word subset sumset Suppose surface T-numbers torus tree uniformly distributed uniformly distributed mod uniformly distributed sequence uniformly maldistributed vectors xero