A Lower Bound in an Approximation Problem Involving the Zeros of the Riemann Zeta Function
نویسنده
چکیده
We slightly improve the lower bound of Báez-Duarte, Balazard, Landreau and Saias in the Nyman-Beurling formulation of the Riemann Hypothesis as an approximation problem. We construct Hilbert space vectors which could prove useful in the context of the so-called “Hilbert-Pólya idea”. Université de NiceSophia Antipolis Laboratoire J.-A. Dieudonné Parc Valrose F-06108 Nice Cedex 02 France [email protected]
منابع مشابه
Landau-siegel Zeros and Zeros of the Derivative of the Riemann Zeta Function
We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.
متن کاملAn Asymptotic Formula for a Sum Involving Zeros of the Riemann Zeta-function
E. Landau gave an interesting asymptotic formula for a sum involving zeros of the Riemann zeta-function. We give an asymptotic formula which can be regarded as a smoothed version of Landau’s formula.
متن کاملFinite Euler Products and the Riemann Hypothesis
Abstract. We show that if the Riemann Hypothesis is true, then in a region containing most of the right-half of the critical strip, the Riemann zeta-function is well approximated by short truncations of its Euler product. Conversely, if the approximation by products is good in this region, the zeta-function has at most finitely many zeros in it. We then construct a parameterized family of non-a...
متن کاملLower bound for the maximum of some derivative of Hardy’s function
Under the Riemann hypothesis, we use the distribution of zeros of the zeta function to get a lower bound for the maximum of some derivative of Hardy’s function.
متن کاملGaps between consecutive zeros of the Riemann zeta-function
An important problem in number theory is to study the distribution of the non-trivial zeros of the Riemann zeta-function which, if one is willing to assume the Riemann Hypothesis, all lie on a vertical line. It is relatively easy to count how many of these zeros lie in a large interval, so the average spacing between consecutive zeros is easy to compute. However, it is a difficult and interesti...
متن کامل