Metric diophantine approximation with two restricted variables. III: Two prime numbers

DOI10.1016/0022-314X(88)90112-6zbMath0655.10049MaRDI QIDQ1109072

Glyn Harman

Publication date: 1988

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

primesnumber of solutionsKloosterman sumssievesdiophantine inequalitymetric diophantine approximation

Mathematics Subject Classification ID

Diophantine approximation in probabilistic number theory (11K60) Homogeneous approximation to one number (11J04) Sieves (11N35)

Related Items (11)

Primes of the form \(\lfloor \alpha p+\beta \rfloor\) ⋮ Primes of the form \([c^ p\)] ⋮ Primes of the form [p^c and related questions] ⋮ Diophantine approximation on lines in \(\mathbb {C}^2\) with Gaussian prime constraints ⋮ Numbers badly approximate by fractions with prime denominator ⋮ RESTRICTED SIMULTANEOUS DIOPHANTINE APPROXIMATION ⋮ UNSOLVED PROBLEMS ⋮ Inhomogeneous Diophantine approximation with prime constraints ⋮ Piatetski‐Shapiro prime k ‐tuplets ⋮ Khintchine’s theorem with rationals coming from neighborhoods in different places ⋮ Metrical theorems on restricted Diophantine approximations to points on a curve.

Cites Work

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• On the metric theory of diophantine approximation
• On the distribution of the convergents of almost all real numbers
• Khintchine's problem in metric diophantine approximation
• Metric Diophantine approximation with two restricted variables. IV. Miscellaneous results
• A note on |αp - q|
• Diophantine approximation with almost‐primes and sums of two squares
• Some theorems in the metric theory of diophantine approximation
• Metric Diophantine approximation with two restricted variables I. Two square-free integers, or integers in arithmetic progressions
• Two remarks in prime number theory
• Diophantine Approximation with a Prime and an Almost-Prime
• Metrical Theorems on Fractional Parts of Sequences

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