Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the distribution of spacings between zeros of the zeta function


Author: A. M. Odlyzko
Journal: Math. Comp. 48 (1987), 273-308
MSC: Primary 11M26; Secondary 11-04, 11Y35
MathSciNet review: 866115
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A numerical study of the distribution of spacings between zeros of the Riemann zeta function is presented. It is based on values for the first $ {10^5}$ zeros and for zeros number $ {10^{12}} + 1$ to $ {10^{12}} + {10^5}$ that are accurate to within $ \pm {10^{ - 8}}$, and which were calculated on the Cray-1 and Cray X-MP computers. This study tests the Montgomery pair correlation conjecture as well as some further conjectures that predict that the zeros of the zeta function behave like eigenvalues of random Hermitian matrices. Matrices of this type are used in modeling energy levels in physics, and many statistical properties of their eigenvalues are known. The agreement between actual statistics for zeros of the zeta function and conjectured results is generally good, and improves at larger heights. Several initially unexpected phenomena were found in the data and some were explained by relating them to the primes.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11M26, 11-04, 11Y35

Retrieve articles in all journals with MSC: 11M26, 11-04, 11Y35


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1987-0866115-0
PII: S 0025-5718(1987)0866115-0
Article copyright: © Copyright 1987 American Mathematical Society