An explicit density estimate





Submitted in 2009.




The number of co-authors is unusual in the field of Number Theory (and in Pure Mathematics too) but it reflects a political decision against a certain policy of systematical bibliometrical evaluation. Indeed bibliometrical informations are starting to be used systematically.

For instance, a three pages long paper with 582 co-authors has thus served as a basis to distribute to one of its author a huge part of the department budget in Lyon. In front of the uproar, this university has finally given up on this decision, but only for this year. Several similar steps are being taken, and in other European countries as well.

This paper is not a trick and is completely correct. It can be seen as a natural mutation to get adapted to this everchanging world.


In this paper, we prove an explicit upper bound for the number of zeros for L-functions, whose imaginary part is less than T and real part larger than σ>1/2.







The previous text is not the published one. For it should not be quoted. Reprints of published version may be asked by e-mails.