Results 1 - 10 of 521
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[en] We prove a new density theorem for the zeros of the Riemann zeta-function in the critical strip, and apply it to the problem of the number of sign changes of the argument of the zeta-function on almost all short intervals of the critical line
[en] We obtain a new estimate for the number of zeros ρn=βn+iγn of the Riemann zeta-function, 14<γ1<γ2< ... ≤<γn≤<γn+1≤..., whose ordinates <γn belong to a given interval and for which the difference <γn+r-<γn is sufficiently large in comparison with the 'mean' value 2πr(ln(<γn/2π))-1
[en] A certain new symmetric representation of Riemann's xi function is considered. A theorem on the zeros of trigonometric integrals analogous to Kakeya's theorem on the zeros of polynomials with monotonically non-decreasing coefficients is used. A modification of Polya's method is suggested, which allows one to obtain new assertions on the disposition of the zeros of the zeta function
[en] An elementary approach for computing the values at negative integers of the Riemann zeta function is presented. The approach is based on a new method for ordering the integers. We show that the values of the Riemann zeta function can be computed, without using the theory of analytic continuation and any knowledge of functions of complex variable.