On the determinant of an integral lattice generated by rational approximants of the Euler constant
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A. I. Aptekarev and D. N. Tulyakov
Translated by: Alex Martsinkovsky - Trans. Moscow Math. Soc. 2009, 237-249
- DOI: https://doi.org/10.1090/S0077-1554-09-00175-7
- Published electronically: December 3, 2009
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Abstract:
We investigate rational approximants of the Euler constant constructed using a certain system of jointly orthogonal polynomials and “averaging” such approximants of mediant type. The properties of such approximants are related to the properties of an integral lattice in $\mathbb R^3$ constructed from recurrently generated sequences. We also obtain estimates on the metric properties of a reduced basis, which imply that the $\gamma$-forms with coefficients constructed from basis vectors of the lattice tend to zero. The question of whether the Euler constant is irrational is reduced to a property of the bases of lattices.References
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Bibliographic Information
- A. I. Aptekarev
- Affiliation: M. V. Keldysh Institute of Applied Mathematics, 4 Miusskaya Ploshchad′, Moscow 125047, Russia, and Lomonosov State University, Moscow, Russia
- MR Author ID: 192572
- Email: aptekaa@keldysh.ru
- D. N. Tulyakov
- Affiliation: M. V. Keldysh Institute of Applied Mathematics, 4 Miusskaya Ploshchad′, Moscow 125047, Russia
- MR Author ID: 632175
- Published electronically: December 3, 2009
- Additional Notes: Partially supported by RFFI, Project No. 08–01–00179, Program No. 1 OMN RAN, and the Support Program for Leading Scientific Schools (Project NSh–3906.2008.1).
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2009, 237-249
- MSC (2000): Primary 11J72; Secondary 33C45, 41A21
- DOI: https://doi.org/10.1090/S0077-1554-09-00175-7
- MathSciNet review: 2573642