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ArticleOriginal scientific text

Title

Classes of polynomials having only one non-cyclotomic irreducible factor

Authors 1, 2, 3, 2

Affiliations

  1. Department of Mathematics, Penn State University, University Park, PA 16802, U.S.A.
  2. Mathematics Department, University of South Carolina, Columbia, SC 29208, U.S.A.
  3. Department of Mathematics, University of California, Berkeley, CA 94720-3840, U.S.A.

Bibliography

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  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.
Acta Arithmetica
1999/90/2
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Pages:
121-153
Main language of publication
English
Received
1998-07-24
Published
1999
Exact and natural sciences