TY - JOUR
T1 - The prime number race and zeros of dirichlet L-functions off the critical line
T2 - Part III
AU - Ford, Kevin
AU - Lamzouri, Youness
AU - Konyagin, Sergei
N1 - Funding Information:
The research of K.F. was partially supported by National Science Foundation grant DMS-0901339. The research of S.K. was partially supported by Russian Fund for Basic Research, Grant N. 11-01-00329. The research of Y.L. was supported by a Postdoctoral Fellowship from the Natural Sciences and Engineering Research Council of Canada.
PY - 2013/12
Y1 - 2013/12
N2 - We show, for any q≥3 and distinct reduced residues a, b (mod q), that the existence of certain hypothetical sets of zeros of Dirichlet L-functions lying off the critical line implies that π(x; q, a)<π(x; q, b) for a set of real x of asymptotic density 1.
AB - We show, for any q≥3 and distinct reduced residues a, b (mod q), that the existence of certain hypothetical sets of zeros of Dirichlet L-functions lying off the critical line implies that π(x; q, a)<π(x; q, b) for a set of real x of asymptotic density 1.
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U2 - 10.1093/qmath/has021
DO - 10.1093/qmath/has021
M3 - Article
AN - SCOPUS:84890771297
SN - 0033-5606
VL - 64
SP - 1091
EP - 1098
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 4
ER -