Classes of polynomials having only one non-cyclotomic irreducible factor

• Autorzy: A. Borisov , M. Filaseta , T. Y. Lam , O. Trifonov
• Języki publikacji: EN

Kategorie tematyczne

• 11C08: Polynomials
• 11S05: Polynomials
• 11R09: Polynomials (irreducibility, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 90
• Numer: 2
• Strony: 121-153

Daty

wydano

1999

otrzymano

1998-07-24

Twórcy

autor

A. Borisov

• Department of Mathematics, Penn State University, University Park, PA 16802, U.S.A.

autor

M. Filaseta

• Mathematics Department, University of South Carolina, Columbia, SC 29208, U.S.A.

autor

T. Y. Lam

• Department of Mathematics, University of California, Berkeley, CA 94720-3840, U.S.A.

autor

O. Trifonov

• Mathematics Department, University of South Carolina, Columbia, SC 29208, U.S.A.

Bibliografia

• [1] A. Baker, Transcendental Number Theory, Cambridge Univ. Press, Cambridge, 1979.
• [2] A. Borisov, On some polynomials allegedly related to the abc conjecture, Acta Arith. 84 (1998), 109-128.
• [3] F. Q. Gouvêa, p-adic Numbers, An Introduction, Springer, Berlin, 1997.
• [4] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, A Foundation for Computer Science, Addison-Wesley, Reading, Mass., 1989.
• [5] E. Gutkin, Billiard Tables of Constant Width and Dynamical Characterizations of the Circle, Abstract, Penn State Workshop, October, 1993.
• [6] N. Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions, Springer, New York, 1977.
• [7] L. J. Mordell, Diophantine Equations, Academic Press, London, 1969.
• [8] J.-L. Nicolas et A. Schinzel, Localisation des zéros de polynômes intervenant en théorie du signal, in: Cinquante ans de polynômes (Paris, 1988), Lecture Notes in Math. 1415, Springer, Berlin, 1990, 167-179.
• [9] G. Pólya and G. Szegö, Problems and Theorems in Analysis I, Springer, New York, 1972.
• [10] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-89.
• [11] I. Schur, Einige Sätze über Primzahlen mit Anwendungen auf Irreduzibilitätsfragen. I, Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 1929, 125-136.
• [12] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Math. 87, Cambridge Univ. Press, Cambridge, 1986.
• [13] J. J. Sylvester, On arithmetical series, Messenger of Math. 21 (1892), 1-19.
• [14] L. Washington, Cyclotomic Fields, Springer, New York, 1997.
• [15] E. Weiss, Algebraic Number Theory, Chelsea, New York, 1963.