Distribution of solutions of diophantine equations f 1 ( x 1 ) f 2 ( x 2 ) = f 3 ( x 3 ) , where f i are polynomials

A. Schinzel; U. Zannier

Rendiconti del Seminario Matematico della Università di Padova (1992)

  • Volume: 87, page 39-68
  • ISSN: 0041-8994

How to cite

top

Schinzel, A., and 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 87 (1992): 39-68. <http://eudml.org/doc/108258>.

@article{Schinzel1992,
author = {Schinzel, A., Zannier, U.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {polynomials with integer coefficients; number of solutions; quadratic polynomials; lower bound},
language = {eng},
pages = {39-68},
publisher = {Seminario Matematico of the University of Padua},
title = {Distribution of solutions of diophantine equations $f_1(x_1)f_2(x_2) = f_3(x_3)$, where $f_i$ are polynomials},
url = {http://eudml.org/doc/108258},
volume = {87},
year = {1992},
}

TY - JOUR
AU - Schinzel, A.
AU - Zannier, U.
TI - Distribution of solutions of diophantine equations $f_1(x_1)f_2(x_2) = f_3(x_3)$, where $f_i$ are polynomials
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1992
PB - Seminario Matematico of the University of Padua
VL - 87
SP - 39
EP - 68
LA - eng
KW - polynomials with integer coefficients; number of solutions; quadratic polynomials; lower bound
UR - http://eudml.org/doc/108258
ER -

References

top
  1. [1] E. Bombieri - J. PILA, The number of integral points on arcs and ovals, Duke Math. J., 52 (1989), pp. 337-357. Zbl0718.11048MR1016893
  2. [2] R.D. Carmichael, On the numerical factors of the arithmetic form αn ± βn, Ann. Math. (2), 15 (1913-1914), pp. 30-70. JFM44.0216.01
  3. [3] P.G.L. Dirichlet, Vorlesungen über Zahlentheorie, 4 Auflage, reprint Chelsea, New York (1968). MR237283
  4. [4] F. Dodd - L. Mattics, Solution of the problem E 3138, Amer. Math. Monthly. 
  5. [5] M.N. Huxley, A note on polynomial congruences, Recent Progress in Analytic Number Theory, Vol. 1 (Durham1979), pp. 193-196, Academic Press (1981). Zbl0463.10002MR637347
  6. [6] B.W. Jones, The Arithmetic Theory of Quadratic Forms, J. Wiley, New York (1950). Zbl0041.17505MR37321
  7. [7] O. Perron, Die Lehre von den Kettenbrüchen, 2 Auflage, reprint Chelsea. Zbl0041.18206
  8. [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. Zbl0475.10034
  9. [9] G. Sándor, Über die Anzahl der Lösungen einer Kongruenz, Acta Math., 87 (1952), pp. 13-16. Zbl0046.26605MR47679
  10. [10] A. Schinzel, On some problems of the arithmetical theory of continued fractions, Acta Arith., 7 (1961), pp. 393-413. Zbl0099.04003MR125814
  11. [11] A. Schinzel, Selected Topics of Polynomials, The University of Michigan Press, Ann Arbor (1982). Zbl0487.12002MR649775
  12. [12] D. Wolke, Multiplikative Funktionen auf schnell wachsenden Folgen, J. Reine Angew. Math., 251 (1971), pp. 55-67. Zbl0234.10030MR289439

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.