Distribution of solutions of diophantine equations f 1 (x 1 )f 2 (x 2 )=f 3 (x 3 ), where f i are polynomials
Schinzel, A. ; Zannier, U.
Rendiconti del Seminario Matematico della Università di Padova, Tome 88 (1992), p. 39-68 / Harvested from Numdam
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@article{RSMUP_1992__87__39_0,
     author = {Schinzel, A. and Zannier, Umberto},
     title = {Distribution of solutions of diophantine equations $f\_1(x\_1)f\_2(x\_2) = f\_3(x\_3)$, where $f\_i$ are polynomials},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {88},
     year = {1992},
     pages = {39-68},
     mrnumber = {1183901},
     zbl = {0762.11011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1992__87__39_0}
}

Schinzel, A.; Zannier, U. Distribution of solutions of diophantine equations $f_1(x_1)f_2(x_2) = f_3(x_3)$, where $f_i$ are polynomials. Rendiconti del Seminario Matematico della Università di Padova, Tome 88 (1992) pp. 39-68. http://gdmltest.u-ga.fr/item/RSMUP_1992__87__39_0/

[1] E. Bombieri - J. PILA, The number of integral points on arcs and ovals, Duke Math. J., 52 (1989), pp. 337-357. | MR 1016893 | Zbl 0718.11048

[2] R.D. Carmichael, On the numerical factors of the arithmetic form αn ± βn, Ann. Math. (2), 15 (1913-1914), pp. 30-70. | JFM 44.0216.01

[3] P.G.L. Dirichlet, Vorlesungen über Zahlentheorie, 4 Auflage, reprint Chelsea, New York (1968). | MR 237283

[4] F. Dodd - L. Mattics, Solution of the problem E 3138, Amer. Math. Monthly.

[5] M.N. Huxley, A note on polynomial congruences, Recent Progress in Analytic Number Theory, Vol. 1 (Durham 1979), pp. 193-196, Academic Press (1981). | MR 637347 | Zbl 0463.10002

[6] B.W. Jones, The Arithmetic Theory of Quadratic Forms, J. Wiley, New York (1950). | MR 37321 | Zbl 0041.17505

[7] O. Perron, Die Lehre von den Kettenbrüchen, 2 Auflage, reprint Chelsea. | Zbl 0041.18206

[8] G. Robin, Estimation de la fonction de Tchebychef Θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n, Acta Arith., 42 (1983), pp. 367-389. | Zbl 0475.10034

[9] G. Sándor, Über die Anzahl der Lösungen einer Kongruenz, Acta Math., 87 (1952), pp. 13-16. | MR 47679 | Zbl 0046.26605

[10] A. Schinzel, On some problems of the arithmetical theory of continued fractions, Acta Arith., 7 (1961), pp. 393-413. | MR 125814 | Zbl 0099.04003

[11] A. Schinzel, Selected Topics of Polynomials, The University of Michigan Press, Ann Arbor (1982). | MR 649775 | Zbl 0487.12002

[12] D. Wolke, Multiplikative Funktionen auf schnell wachsenden Folgen, J. Reine Angew. Math., 251 (1971), pp. 55-67. | MR 289439 | Zbl 0234.10030