Solved and unsolved problems οn polynomials

Andrzej Schinzel

Banach Center Publications (1995)

  • Volume: 34, Issue: 1, page 149-159
  • ISSN: 0137-6934

How to cite

top

Schinzel, Andrzej. "Solved and unsolved problems οn polynomials." Banach Center Publications 34.1 (1995): 149-159. <http://eudml.org/doc/251347>.

@article{Schinzel1995,
author = {Schinzel, Andrzej},
journal = {Banach Center Publications},
keywords = {complex polynomials; roots; sporadic polynomials; expository lecture; polynomials of a single variable; factorization; lower bounds; nonzero coefficients; reducibility},
language = {eng},
number = {1},
pages = {149-159},
title = {Solved and unsolved problems οn polynomials},
url = {http://eudml.org/doc/251347},
volume = {34},
year = {1995},
}

TY - JOUR
AU - Schinzel, Andrzej
TI - Solved and unsolved problems οn polynomials
JO - Banach Center Publications
PY - 1995
VL - 34
IS - 1
SP - 149
EP - 159
LA - eng
KW - complex polynomials; roots; sporadic polynomials; expository lecture; polynomials of a single variable; factorization; lower bounds; nonzero coefficients; reducibility
UR - http://eudml.org/doc/251347
ER -

References

top
  1. [1] A. Capelli, Sulla riduttibilita delle equazioni algebriche, Nota prima, Rend. Accad. Fis. Mat. Soc. Napoli (3), 3 (1897), 243-252. Zbl28.0090.01
  2. [2] D. Coppersmith and J. Davenport, Polynomials whose powers are sparse, Acta Arith. 58 (1991), 79-87. Zbl0729.11015
  3. [3] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith. 34 (1979), 391-401. Zbl0416.12001
  4. [4] F. Dorey and G. Whaples, Prime and composite polynomials, J. Algebra 28 (1974), 88-101. Zbl0286.12102
  5. [5] A. Dubickas, On a conjecture of A. Schinzel and H. Zassenhaus, Acta Arith. 63 (1993), 15-20. 
  6. [6] P. Erdős, On the number of terms of the square of a polynomial, Nieuw. Arch. Wiskunde (2) 23 (1949), 63-65. Zbl0032.00203
  7. [7] M. Fried and R. E. MacRae, On the invariance of the chain of fields, Illinois J. Math. 13 (1969), 165-171. Zbl0174.07302
  8. [8] K. Győry and A. Schinzel, On a conjecture of Posner and Rumsey, J. Number Theory 47 (1994), 63-78. Zbl0813.11061
  9. [9] D. H. Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. 34 (1933), 461-479. Zbl0007.19904
  10. [10] R. Louboutin, Sur la mesure de Mahler d'un nombre algébrique, C. R. Acad. Sci. Paris, Sér. I 296 (1983), 539-542. Zbl0557.12001
  11. [11] L. Rédei, Algebra, Erster Teil, Akademische Verlaggesellschaft, Leipzig, 1959. 
  12. [12] A. Rényi, On the minimal number of terms in the square of a polynomial, Hungar. Acta Math. 1 (1947), 30-34 = Selected papers, vol. 1, Budapest 1976, 42-47. Zbl0030.11402
  13. [13] J. F. Ritt, Prime and composite polynomials, Trans. Amer. Math. Soc., 23 (1922), 51-66. Zbl48.0079.01
  14. [14] A. Schinzel, Reducibility of lacunary polynomials I, Acta Arith. 16 (1969), 123-159. 
  15. [15] A. Schinzel, Selected topics on polynomials, The University of Michigan Press, Ann Arbor, 1982. 
  16. [16] A. Schinzel, On the number of terms of a power of a polynomial, Acta Arith. 49 (1987), 55-70. Zbl0632.12024
  17. [17] A. Schinzel, On reducible trinomials, Dissertationes Math. 329 (1993). 
  18. [18] A. Schinzel and H. Zassenhaus, A refinement of two theorems of Kronecker, Michigan Math. J. 12 (1965), 81-85. Zbl0128.03402
  19. [19] C. J. Smyth, On the product of the conjugates outside the unit circle of an algebraic integer, Bull. London Math. Soc. 3 (1971), 169-175. Zbl0235.12003
  20. [20] W. Verdenius, On the number of terms of the square and the cube of polynomials, Indag. Math. 11 (1949), 459-465. Zbl0038.01101
  21. [21] U. Zannier, Ritt's second theorem for arbitrary characteristic, J. Reine Angew. Math. 445 (1993), 175-203. Zbl0786.12001

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.