N. I. Fel'dman, “Effective bounds for the number of solutions of certain diophantine equations”, Mat. Zametki, 8:3 (1970), 361–371; Math. Notes, 8:3 (1970), 674

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Matematicheskie Zametki, 1970, Volume 8, Issue 3, Pages 361–371 (Mi mzm9571)

This article is cited in 5 scientific papers (total in 6 papers)

Effective bounds for the number of solutions of certain diophantine equations

N. I. Fel'dman

M. V. Lomonosov Moscow State University

Full-text PDF (939 kB) Citations (6)

Abstract: It is proved that the number of solutions of the diophantine equation

N o r m (z_{1} ω_{1} + \dots + z_{m} ω_{m}) = f (z_{1}, \dots, z_{m}),

$\mathrm{Norm}\,(z_1\omega_1+\dots+z_m\omega_m)=f(z_1,\dots,z_m),$
is finite, where

ω_{1}, \dots, ω_{m}

$\omega_1,\dots,\omega_m$ are algebraic numbers of a special type, the left side of the equation is the norm with respect to a quadratic field, and

f

$f$ is a low-degree polynomial.

Received: 25.06.1969

English version:
Mathematical Notes, 1970, Volume 8, Issue 3, Pages 674–679
DOI: https://doi.org/10.1007/BF01159064

Bibliographic databases:

Document Type: Article

UDC: 511

Language: Russian

Citation: N. I. Fel'dman, “Effective bounds for the number of solutions of certain diophantine equations”, Mat. Zametki, 8:3 (1970), 361–371; Math. Notes, 8:3 (1970), 674–679

Citation in format AMSBIB

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\by N.~I.~Fel'dman

\paper Effective bounds for the number of solutions of certain diophantine equations

\jour Mat. Zametki

\yr 1970

\vol 8

\issue 3

\pages 361--371

\mathnet{http://mi.mathnet.ru/mzm9571}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=272709}

\zmath{https://zbmath.org/?q=an:0211.37603}

\transl

\jour Math. Notes

\yr 1970

\vol 8

\issue 3

\pages 674--679

\crossref{https://doi.org/10.1007/BF01159064}

Linking options:

https://www.mathnet.ru/eng/mzm9571

https://www.mathnet.ru/eng/mzm/v8/i3/p361

This publication is cited in the following 6 articles:

N. Saradha, Divyum Sharma, “Simultaneous rational approximation via Rickert's integrals”, Indagationes Mathematicae, 26:1 (2015), 88
Michael A. Bennett, “Solving Norm Form Equations Via Lattice Basis Reduction”, Rocky Mountain J. Math., 26:3 (1996)
N. M. Korobov, Yu. V. Nesterenko, A. B. Shidlovskii, “Naum Il'ich Feld'man (obituary)”, Russian Math. Surveys, 50:6 (1995), 1247–1252
John H. Rickert, “Simultaneous rational approximations and related diophantine equations”, Math. Proc. Camb. Phil. Soc., 113:3 (1993), 461
E. M. Matveev, “Linear forms in the values of $G$ -functions, and Diophantine equations”, Math. USSR-Sb., 45:3 (1983), 379–396
V. G. Sprindzhuk, “Achievements and problems in Diophantine approximation theory”, Russian Math. Surveys, 35:4 (1980), 1–80

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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