A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis III. Exponential weight functions

Details A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis III. Exponential weight functions A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis III. Exponential weight functions

2010-06-02

arxiv.org/abs/1006.0323v1

Mathematics

Number Theory

Scientific paper

This paper is a continuation of our recent papers with the same title, arXiv:0806.1596v1 [math.NT], arXiv:0904.1277v1 where a number of integral equalities involving integrals of the logarithm of the Riemann zeta-function were introduced and it was shown that some of them are equivalent to the Riemann hypothesis. A few new equalities of this type, which this time involve exponential functions, are established, and for the first time we have found such equalities involving the integrals of the logarithm of the Riemann zeta-function taken exclusively along the real axis. Some of the obtained equalities are tested numerically. In particular, an integral equality involving the logarithm of the module of zeta(1/2+i*t) and a weight function cosh**(-1)(pi*t) is shown numerically to be correct up to the 80 digits. For exponential weight function, the possible contribution of the Riemann function zeroes non-lying on the critical line is rigorously estimated and shown to be extremely small.

Affiliated with

Also associated with

No associations

Rating

A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis III. Exponential weight functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis III. Exponential weight functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A few equalities involving integrals of the logarithm of the Riemann zeta-function and equivalent to the Riemann hypothesis III. Exponential weight functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-512652