THE DISTRIBUTION OF ROOTS OF A POLYNOMIAL

Granville, Andrew

doi:10.1007/978-1-4020-5404-4_6

Andrew Granville³

Part of the book series: NATO Science Series ((NAII,volume 237))

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Abstract

How are the roots of a polynomial distributed (in ℂ)? The question is too vague for if one chooses one’s favourite complex numbers z₁, z₂, ⋯, z_d then the polynomial Π^d _j=1(x - z_j) has its roots at these points.

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References

Bilu, Y. (1997) Limit distribution of small points on algebraic tori, Duke Math. J. 89, 465–476.
Article MATH MathSciNet Google Scholar
Bombieri, E. and Zannier, U. (1995) Algebraic points on subvarieties of Gⁿ _m, Internat. Math. Res. Notices 1995, 333–347.
Article MATH MathSciNet Google Scholar
Dobrowolski, E. (1979) On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith 34, 391–01.
MATH MathSciNet Google Scholar
Erdős, P. and Turán, P. (1950) On the distribution of roots of polynomials, Ann. Math. 51, 105–119.
Article Google Scholar
Hughes, C. and Nikeghbali, A. (2006) The zeros of random polynomials cluster uniformly near the unit circle, to appear.
Google Scholar
Lehmer, D. H. (1933) Factorization of certain cyclotomic functions, Ann. Math. 34, 461–479.
Article MathSciNet Google Scholar
Rumely, R. (1999) On Bilu’s equidistribution theorem, Contemp. Math. 237, 159–166.
MathSciNet Google Scholar
Ullmo, E. (2006) Manin—Mumford, André—Oort, the equidistribution point of view, in this book.
Google Scholar
Zagier, D. (1993) Algebraic numbers close to both 0 and 1, Math. Comp. 61, 485–491.
Article MATH MathSciNet Google Scholar
Zhang, S. (1995) Positive line bundles on arithmetic varieties, J. Amer. Math. Soc. 8, 187–221.
Article MathSciNet Google Scholar

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Authors and Affiliations

Université de Montréal, Montréal
Andrew Granville

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Andrew Granville
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Editors and Affiliations

University of Montréal, QC,, Canada
Andrew Granville
Tel-Aviv University, Israel
Zeév Rudnick

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Granville, A. (2007). THE DISTRIBUTION OF ROOTS OF A POLYNOMIAL. In: Granville, A., Rudnick, Z. (eds) Equidistribution in Number Theory, An Introduction. NATO Science Series, vol 237. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5404-4_6

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DOI: https://doi.org/10.1007/978-1-4020-5404-4_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-5402-0
Online ISBN: 978-1-4020-5404-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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