Diophantine approximation with arithmetic functions, II
نویسندگان
چکیده
منابع مشابه
Diophantine Approximation with Arithmetic Functions, Ii
We prove that real numbers can be well-approximated by the normalized Fourier coefficients of newforms.
متن کاملDiophantine Approximation with Arithmetic Functions, I
We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.
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Let α be an irrational and φ : N → R be a function decreasing to zero. For any α with a given Diophantine type, we show some sharp estimations for the Hausdorff dimension of the set Eφ(α) := {y ∈ R : ‖nα− y‖ < φ(n) for infinitely many n}, where ‖ · ‖ denotes the distance to the nearest integer.
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DIOPHANTINE EQUATIONS INVOLVING ARITHMETIC FUNCTIONS OF FACTORIALS Daniel M. Baczkowski We examine and classify the solutions to certain Diophantine equations involving factorials and some well known arithmetic functions. F. Luca has showed that there are finitely many solutions to the equation:
متن کاملDiophantine Approximation of Ternary Linear Forms . II
Let 6 denote the positive root of the equation xs + x2 — 2x — 1 = 0; that is, 8 = 2 cos(27r/7). The main result of the paper is the evaluation of the constant lim supm-co min M2\x + By + 02z|, where the min is taken over all integers x, y, z satisfying 1 g max (\y\, |z|) g M. Its value is (29 + 3),/7 = .78485. The same method can be applied to other constants of the same type.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2009
ISSN: 0024-6093
DOI: 10.1112/blms/bdp051