We prove that there are absolute constants and such that for every
there are
such that
has at least distinct sign changes in . This improves and extends earlier results of Bloch and Pólya.
Nous prouvons qu’il existe des constantes absolues et telles que pour tout
il existe
tels que
a au moins changements de signe distincts dans . Cela améliore et étend des résultats antérieurs de Bloch et Pólya.
@article{JTNB_2008__20_2_281_0, author = {Erd\'elyi, Tam\'as}, title = {Extensions of the {Bloch{\textendash}P\'olya} theorem on the number of real zeros of polynomials}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {281--287}, publisher = {Universit\'e Bordeaux 1}, volume = {20}, number = {2}, year = {2008}, doi = {10.5802/jtnb.627}, zbl = {1163.11022}, mrnumber = {2477504}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.627/} }
TY - JOUR AU - Erdélyi, Tamás TI - Extensions of the Bloch–Pólya theorem on the number of real zeros of polynomials JO - Journal de théorie des nombres de Bordeaux PY - 2008 SP - 281 EP - 287 VL - 20 IS - 2 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.627/ DO - 10.5802/jtnb.627 LA - en ID - JTNB_2008__20_2_281_0 ER -
%0 Journal Article %A Erdélyi, Tamás %T Extensions of the Bloch–Pólya theorem on the number of real zeros of polynomials %J Journal de théorie des nombres de Bordeaux %D 2008 %P 281-287 %V 20 %N 2 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.627/ %R 10.5802/jtnb.627 %G en %F JTNB_2008__20_2_281_0
Erdélyi, Tamás. Extensions of the Bloch–Pólya theorem on the number of real zeros of polynomials. Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 2, pp. 281-287. doi : 10.5802/jtnb.627. http://www.numdam.org/articles/10.5802/jtnb.627/
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