Perturbed moments and a longer mollifier for critical zeros of $$\zeta $$ ζ
نویسندگان
چکیده
منابع مشابه
ON THE ZEROS OF ζ (s) NEAR THE CRITICAL LINE
Let ρ = β ′ + iγ ′ denote the zeros of ζ (s), s = σ + i t . It is shown that there is a positive proportion of the zeros of ζ (s) in 0 < t < T satisfying β ′ − 1/2 (log T )−1. Further results relying on the Riemann hypothesis and conjectures on the gaps between the zeros of ζ(s) are also obtained.
متن کاملZeros 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...
متن کاملZeros of Dedekind zeta functions in the critical strip
In this paper, we describe a computation which established the GRH to height 92 (resp. 40) for cubic number fields (resp. quartic number fields) with small discriminant. We use a method due to E. Friedman for computing values of Dedekind zeta functions, we take care of accumulated roundoff error to obtain results which are mathematically rigorous, and we generalize Turing’s criterion to prove t...
متن کاملZeros of Lattice Sums Zeros of Epstein Zeta Functions off the Critical Line
We consider zeros of two-dimensional sums over rectangular lattices, and in particular a sum first studied by Potter and Titchmarsh in 1935. They proved several properties of the zeros of sums over the rectangular lattice, and commented on the fact that a particular sum had zeros off the critical line. We investigate the behaviour of one such zero as a function of the ratio of the periods of th...
متن کاملDistribution of the zeros of the Riemann zeta function in longer intervals
In this paper, we extend the result of Fujii on the second moment of S(t + h) − S(t) to longer range of h under the Riemann Hypothesis and an quantitative form of the Twin Prime Conjecture.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Research in Number Theory
سال: 2018
ISSN: 2522-0160,2363-9555
DOI: 10.1007/s40993-018-0103-4