Geodesic
Elementary Symmetric Polynomials in Numbers of Modulus 1
Canadian journal of mathematics, Tome 54 (2002) no. 2, pp. 239-262

Voir la notice de l'article provenant de la source Cambridge University Press

We describe the set of numbers ${{\sigma }_{k}}\left( {{z}_{1}},\cdot \cdot \cdot ,{{z}_{n+1}} \right)$ , where ${{z}_{1}},\cdot \cdot \cdot ,{{z}_{n+1}}$ are complex numbers of modulus 1 for which ${{z}_{1}}{{z}_{2}}\cdot \cdot \cdot {{z}_{n+1}}=1$ , and ${{\sigma }_{k}}$ 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 ${{\overset{\sim }{\mathop{\text{A}}}\,}_{n}}$ .
DOI : 10.4153/CJM-2002-008-x
Mots-clés : 05E05, 33C45, 30C15, 51E24 
Cartwright, Donald I.; Steger, Tim. Elementary Symmetric Polynomials in Numbers of Modulus 1. Canadian journal of mathematics, Tome 54 (2002) no. 2, pp. 239-262. doi: 10.4153/CJM-2002-008-x
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