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Lower Bounds on the Largest Inhomogeneous Approximation Constant Cover

Lower Bounds on the Largest Inhomogeneous Approximation Constant

By: Bishnu Paudel and  Chris Pinner  
Open Access
|Feb 2025

References

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  2. DAVENPORT, H.: Indefinite binary quadratic forms, and Euclid’s algorithm in real quadratic fields, Proc. London Math. Soc. 53, no. 2, (1951), 65–82.
  3. ENNOLA, V.: On the first inhomogeneous minimum of indefinite binary quadratic forms, and Euclid’s algorithm in real quadratic fields, Ann. Univ. Turkuensis Ser. AI 28 (1958), 9–58.
  4. FUKASAWA, S.:Über die Grössenordnung des absoluten Betrages von einer linearen inhomogenen Form I, II & IV, Japan J. Math. 3 (1926), 1–26, 91–106 & 4 (1927) 147–167.
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  7. PAUDEL, B.—PINNER, C.: An upper bound on the inhomogeneous approximation constants, Proceedings of the Integers Conference 2023, arXiv 2301.12270 [math.NT], Integers (to appear)
  8. PINNER, C. G.: More on inhomogeneous Diophantine approximation, Journal de Théorie des Nombres, Bordeaux. 13 (2001) no. 2, 539–557.
  9. PINNER, C. G.: Lower bounds on the two-sided inhomogeneous approximation constant, arXiv:1603.06178[math.NT], (2016).
  10. PINNER, C.: On the inhomogeneous spectrum of period two quadratics, arXiv:1603.06179 [math.NT], (2016).
  11. PITMAN, J.: Davenport’s constant for indefinite binary quadratic forms,Acta Arith. 6 (1960), 37–46.
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DOI: https://doi.org/10.2478/udt-2023-0015 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X
Language: English
Page range: 77 - 98
Submitted on: Nov 13, 2023
Accepted on: Dec 20, 2023
Published on: Feb 24, 2025
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2025 Bishnu Paudel, Chris Pinner, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.