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Introduction to Diophantine Approximation
Formalized Mathematics, 2015 Abstract In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the
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Summing μ ( n ) : a faster elementary algorithm. [PDF]
Res Number Theory, 2023 Helfgott HA, Thompson L.
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Diophantine approximation with arithmetic functions, I [PDF]
, 2008 Emré Alkan +2 more
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A Prime Orbit Theorem for Self-Similar Flows and Diophantine Approximation [PDF]
, 2001 Michel L. Lapidus +1 more
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METRICAL PROBLEMS IN DIOPHANTINE APPROXIMATION [PDF]
, 2021 Ayreena Bakhtawar
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On prime powers in linear recurrence sequences. [PDF]
Ann Math Quebec, 2023 Odjoumani J, Ziegler V.
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Rotations by roots of unity and Diophantine approximation [PDF]
, 2016 Romanos-Diogenes Malikiosis
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Sequences of Diophantine approximations
Journal of Number Theory, 1974 AbstractWe sharpen a technique of Gelfond to show that, in a sense, the only possible gap-free sequences of “good” Diophantine approximations to a fixed α ∈ C are trivial ones. For example, suppose that a > 1 and that (δn)n=1∞ and (σn)n=1∞ are two positive, strictly increasing unbounded sequences satisfying δn+1 ≤ aδn and σn+1 ≤ aσn.
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Simultaneous Diophantine approximation to points on the Veronese curve [PDF]
Dzmitry Badziahin
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Unconventional height functions in simultaneous Diophantine approximation. [PDF]
Mon Hefte Math, 2017 Fishman L, Simmons D.
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