Sign Changes of the Liouville Function on Quadratics
Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 251-257
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Let $\text{ }\!\!\lambda\!\!\text{ }\left( n \right)$ denote the Liouville function. Complementary to the prime number theorem, Chowlaconjectured that * $$\sum\limits_{n\le x}{\lambda \,\left( f\left( n \right) \right)}=o\left( x \right)$$ for any polynomial $f\left( x \right)$ with integer coefficients which is not of form $bg{{\left( x \right)}^{2}}$ .
Mots-clés :
11N60, 11B83, 11D09, Liouville function, Chowla's conjecture, prime number theorem, binary sequences, changes sign infinitely often, quadratic polynomials, Pell equations
Borwein, Peter; Choi, Stephen K. K.; Ganguli, Himadri. Sign Changes of the Liouville Function on Quadratics. Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 251-257. doi: 10.4153/CMB-2011-166-9
@article{10_4153_CMB_2011_166_9,
author = {Borwein, Peter and Choi, Stephen K. K. and Ganguli, Himadri},
title = {Sign {Changes} of the {Liouville} {Function} on {Quadratics}},
journal = {Canadian mathematical bulletin},
pages = {251--257},
year = {2013},
volume = {56},
number = {2},
doi = {10.4153/CMB-2011-166-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-166-9/}
}
TY - JOUR AU - Borwein, Peter AU - Choi, Stephen K. K. AU - Ganguli, Himadri TI - Sign Changes of the Liouville Function on Quadratics JO - Canadian mathematical bulletin PY - 2013 SP - 251 EP - 257 VL - 56 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-166-9/ DO - 10.4153/CMB-2011-166-9 ID - 10_4153_CMB_2011_166_9 ER -
%0 Journal Article %A Borwein, Peter %A Choi, Stephen K. K. %A Ganguli, Himadri %T Sign Changes of the Liouville Function on Quadratics %J Canadian mathematical bulletin %D 2013 %P 251-257 %V 56 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-166-9/ %R 10.4153/CMB-2011-166-9 %F 10_4153_CMB_2011_166_9
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