## Applications of number theory to numerical analysis |

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### Contents

Preface v | 1 |

Recurrence Relations and Rational Approximation | 28 |

Uniform Distribution | 48 |

Copyright | |

9 other sections not shown

### Common terms and phrases

algebraic integer algebraic number field approximate solution Bernoulli polynomial bounded variation Cc(a Chap character mod class of functions congruence 9.3 constant implied continued fraction Ct(m cyclotomic field denote the number Df(C Diophantine approximation discrepancy D(n discrepancy Theorem domain error term exists an integral Fibonacci sequence follows by Lemma glp set Hlawka holds Hua Loo Keng independent units induction inequality integers defined integral vector Keng and Wang lemma follows lemma is proved log2 monotonic functions N. M. Korobov number of solutions number theory numerical analysis numerical integration obtain parallelepipeds periodic function positive integer Proo proof of Theorem PV number Qf(C quadrature formula given rational integers rational numbers real algebraic number real number recurrence relation right hand side set of independent set of integers set of points simultaneous Diophantine approximation Suppose Theorem 7.9 theorem follows theorem is proved Wang Yuan x)dx