NEGATIVE VALUES OF THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE
نویسندگان
چکیده
منابع مشابه
Zeros of the Riemann Zeta-Function on the Critical Line
It was shown by Selberg [3] that the Riemann Zeta-function has at least cT log T zeros on the critical line up to height T, for some positive absolute constant c. Indeed Selberg’s method counts only zeros of odd order, and counts each such zero once only, regardless of its multiplicity. With this in mind we shall write γ̂i for the distinct ordinates of zeros of ζ(s) on the critical line of odd m...
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Let ζ(s) be the Riemann zeta function. In this paper, we study repeated values of ζ(s) on the critical line, and we give evidence to support our conjecture that for every nonzero complex number z, the equation ζ(1/2 + it) = z has at most two solutions t ∈ R. We prove a number of related results, some of which are unconditional, and some of which depend on the truth of the Riemann hypothesis. We...
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and some related integrals, where γ denotes imaginary parts of complex zeros of ζ(s), and where every zero is counted with its multiplicity (see also [5] and [7]). The interest is in obtaining unconditional bounds for the above sum, since assuming the Riemann Hypothesis (RH) the sum trivially vanishes. A more general sum than the one in (1.1) was treated by S.M. Gonek [3]. He proved, under the ...
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ژورنال
عنوان ژورنال: Mathematika
سال: 2013
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579313000090