Geodesic
Effectivization of a Lower Bound for $\|(4/3)^k\|$
Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 927-935.

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We obtain an effective lower bound for $\|(4/3)^k\|$, where $\|\cdot\|$ denotes the distance to the nearest integer.
Keywords: Waring's problem, effective lower bound, Beukers estimate, Padé approximation, Stirling's formula.
Mots-clés : effective constant 
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Yu. A. Pupyrev. Effectivization of a Lower Bound for $\|(4/3)^k\|$. Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 927-935. http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a9/

[1] K. Mahler, “On the fractional parts of powers of real numbers. II”, Mathematika, 4 (1957), 122–124 | MR | Zbl

[2] A. Baker, J. Coates, “Fractional parts of powers of rationals”, Math. Proc. Cambridge Philos. Soc., 77 (1975), 269–279 | DOI | MR | Zbl

[3] F. Beukers, “Fractional parts of powers of rationals”, Math. Proc. Cambridge Philos. Soc., 90:1 (1981), 13–20 | DOI | MR | Zbl

[4] A. K. Dubitskas, “Otsenka snizu velichiny $\|(3/2)^k\|$”, UMN, 45:4 (1990), 153–154 | MR | Zbl

[5] F. Delmer, J.-M. Deshouillers, “The computation of $g(k)$ in Waring's problem”, Math. Comp., 54:190 (1990), 885–893 | DOI | MR | Zbl

[6] J. Kubina, M. Wunderlich, “Extending Waring's conjecture up to 471600000”, Math. Comp., 55:192 (1990), 815–820 | DOI | MR | Zbl

[7] M. A. Bennett, “Fractional parts of powers of rational numbers”, Math. Proc. Cambridge Philos. Soc., 114:2 (1993), 191–201 | DOI | MR | Zbl

[8] M. A. Bennett, “An ideal Waring problem with restricted summands”, Acta Arith., 66:2 (1994), 125–132 | MR | Zbl

[9] L. Habsieger, “Explicit lower bounds for $\|(3/2)^k\|$”, Acta Arith., 106:3 (2003), 299–309 | DOI | MR | Zbl

[10] W. Zudilin, “A new lower bound for $\|(3/2)^k\|$”, J. Théor. Nombres Bordeaux, 19:1 (2007), 311–323 | MR | Zbl

[11] L. Schoenfeld, “Sharper bounds for the Chebyshev functions $\theta(x)$ and $\psi(x)$. II”, Math. Comp., 30:134 (1976), 337–360 | DOI | MR | Zbl