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Recurrence Relations and Rational Approximation
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algebraic integer algebraic number field approximate solution Bernoulli polynomial bounded variation Cc(a Chap class of functions constant implied continued fraction cyclotomic field denote the number Df(C Diophantine approximation discrepancy D(n domain eigenvalue error term exists an integral Fibonacci sequence follows by Lemma Fredholm equation glp set Hlawka holds Hua Loo Keng independent units induction inequality integers defined Keng and Wang lemma follows lemma is proved monotonic functions N. M. Korobov N. S. Bahvalov need Lemma number of solutions number theory numerical analysis numerical integration obtain parallelepipeds periodic function positive integer Proo proof of Theorem PV number quadrature formula given rational integers rational numbers real algebraic number real number recurrence relation right hand side set has discrepancy 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