Introduction. In 1974, N. Levinson showed that at least 1/3 of the zeros of the Riemann ζ-function are on the critical line ([19]). Today it is known (Conrey, [6]) that at least 40.77% of the zeros of ζ(s) are on the critical line and at least 40.1% are on the critical line and are simple. In [16] and [17], Hilano showed that Levinson's original result is also valid for Dirichlet L-series. This paper is a shortened version of parts of the dissertation [3], the full details of which may be found at http://www.math.uni-frankfurt.de/~pbauer/diss.ps. We shall prove a mean value theorem for Dirichlet L-series and use this for proving some corollaries concerning the distribution of the zeros of L-series - amongst other results we improve the above mentioned bounds for Dirichlet L-series.
@article{bwmeta1.element.bwnjournal-article-aav93i1p37bwm,
author = {Peter J. Bauer},
title = {Zeros of Dirichlet L-series on the critical line},
journal = {Acta Arithmetica},
volume = {92},
year = {2000},
pages = {37-52},
zbl = {0953.11029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav93i1p37bwm}
}
Peter J. Bauer. Zeros of Dirichlet L-series on the critical line. Acta Arithmetica, Tome 92 (2000) pp. 37-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav93i1p37bwm/
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