The zeros of the Riemann zeta-function

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Simple 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 کامل

Distribution of the zeros of the Riemann Zeta function

One of the most celebrated problem of mathematics is the Riemann hypothesis which states that all the non trivial zeros of the Zeta-function lie on the critical line <(s) = 1/2. Even if this famous problem is unsolved for so long, a lot of things are known about the zeros of ζ(s) and we expose here the most classical related results : all the non trivial zeros lie in the critical strip, the num...

متن کامل

Large Gaps between the Zeros of the Riemann Zeta Function

If the Riemann hypothesis (RH) is true then the non-trivial zeros of the Riemann zeta function, ζ(s), satisfy 1/2+iγn with γn ∈ R. Riemann noted that the argument principle implies that number of zeros of ζ(s) in the box with vertices 0, 1, 1 + iT, and iT is N(T ) ∼ (T/2π) log (T/2πe). This implies that on average (γn+1 − γn) ≈ 2π/ log γn and hence the average spacing of the sequence γ̂n = γn lo...

متن کامل

Hamiltonian for the Zeros of the Riemann Zeta Function.

A Hamiltonian operator H[over ^] is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of H[over ^] is 2xp, which is consistent with the Berry-Keating conjecture. While H[over ^] is not Hermitian in the conventional sense, iH[over ^] is P...

متن کامل

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...

متن کامل

ذخیره 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: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

سال: 1935

ISSN: 1364-5021,1471-2946

DOI: 10.1098/rspa.1935.0146