Linear law for the logarithms of the Riemann periods at simple critical zeta zeros
نویسندگان
چکیده
منابع مشابه
Linear law for the logarithms of the Riemann periods at simple critical zeta zeros
Each simple zero 1 2 + iγn of the Riemann zeta function on the critical line with γn > 0 is a center for the flow ṡ = ξ(s) of the Riemann xi function with an associated period Tn. It is shown that, as γn → ∞, log Tn ≥ π 4 γn +O(log γn). Numerical evaluation leads to the conjecture that this inequality can be replaced by an equality. Assuming the Riemann Hypothesis and a zeta zero separation con...
متن کاملSimple Zeros of the Riemann Zeta-function
Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25% of the zeros of the Riemann zeta-function are simple. Using Montgomery and Taylor's argument together with an elementary combinatorial argument, we prove that assuming the Riemann Hypothesis at least 67.275% of the zeros are simple.
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 کاملOn simple zeros of the Riemann zeta-function
We investigate the distribution of simple zeros of the Riemann zeta-function. Let H ≤ T and L = log T . We calculate in a new way (following old ideas of Atkinson and new ideas of Jutila and Motohashi) the mean square of the product of F (s) = ζ(s) + 1 Lζ ′(s) and a certain Dirichlet polynomial A(s) = ∑ n≤M a(n) ns of length M = T θ with θ < 38 near the critical line: if R is a positive constan...
متن کاملA Study of the Riemann Zeta Zeros
The goals of the proposed research are: 1) To obtain additional concrete computational evidence §2.1 of the unknown structure on the imaginary parts of the non-trivial zeros of the Riemann zeta function, called herein the Riemann spectrum, following the method from [1]; specifically, the PI will compute correlations between histograms of random variables Xp (§2); 2) To prove the that the densit...
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: Mathematics of Computation
سال: 2005
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-05-01803-x