On the distribution of imaginary parts of zeros of the Riemann zeta function, II
نویسنده
چکیده
Mathematics Subject Classification (2000): Primary 11M26; Secondary 11K38 We continue our investigation of the distribution of the fractional parts of αγ, where α is a fixed non-zero real number and γ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta function. We establish some connections to Montgomery’s pair correlation function and the distribution of primes in short intervals. We also discuss analogous results for a more general L-function.
منابع مشابه
On the Distribution of Imaginary Parts of Zeros of the Riemann Zeta Function
There is an intimate connection between the distribution of the nontrivial zeros of the Riemann zeta function ζ(s) and the distribution of prime numbers. Critical to many prime number problems is the horizontal distribution of zeros; here the Riemann Hypothesis (RH) asserts that the zeros all have real part 1 2 . There is also much interest in studying the distribution of the imaginary parts of...
متن کاملMarco’s Repulsion Phenomenon between Zeros of L-functions
We study a subtle inequity in the distribution of differences between imaginary parts of zeros of the Riemann zeta function. We establish a precise measure which explains the phenomenon, first observed by R. P. Marco, that the location of each Riemann zero is encoded in the distribution of large Riemann zeros. We also extend these results to zeros of more general L-functions. In particular, we ...
متن کاملLandau-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 کاملUnnormalized Differences between Zeros of L-functions
We study a subtle inequity in the distribution of unnormalized differences between imaginary parts of zeros of the Riemann zeta function, which was observed by a number of authors. We establish a precise measure which explains the phenomenon, that the location of each Riemann zero is encoded in the distribution of large Riemann zeros. We also extend these results to zeros of more general L-func...
متن کاملOn strategies towards the Riemann Hypothesis : Fractal Supersymmetric QM and a Trace Formula
The Riemann’s hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn = 1/2 + iλn. An improvement of our previous construction to prove the RH is presented by implementing the Hilbert-Polya proposal and furnishing the Fractal Supersymmetric Quantum Mechanical (SUSY-QM) model whose spectrum reproduces the imaginary parts of the zeta zeros. We model the fr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008