Elementary Symmetric Polynomials in Numbers of Modulus 1
2002 ◽
Vol 54
(2)
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pp. 239-262
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Keyword(s):
AbstractWe describe the set of numbers σk(z1,…,zn+1), where z1,…,zn+1 are complex numbers of modulus 1 for which z1z2 … zn+1 = 1, and σk denotes the k-th elementary symmetric polynomial. Consequently, we give sharp constraints on the coefficients of a complex polynomial all of whose roots are of the same modulus. Another application is the calculation of the spectrum of certain adjacency operators arising naturally on a building of type Ãn.
1982 ◽
Vol 59
(3)
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pp. 355-359
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2006 ◽
Vol 204
(2)
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pp. 619-646
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2013 ◽
Vol 89
(3)
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pp. 420-430
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1974 ◽
Vol 8
(3)
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pp. 273-280
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