Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616371 | Journal of Mathematical Analysis and Applications | 2014 | 10 Pages |
Abstract
Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t)S(t) in the theory of the Riemann zeta-function.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
H.M. Bui, S.J. Lester, M.B. Milinovich,