2013/05/31 by Kevin Ford, Alexandru Zaharescu · 5 citations
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Distribution (mathematics) #Explicit formulae #Measure (data warehouse) #Rank (graph theory) #Riemann hypothesis #Riemann zeta function #Zero (linguistics) #math.NT #msc:11K38 #msc:11M26
paper · pdf · doi:10.1112/s0010437x14007659
published in Compositio Mathematica 151(2), 230-252 (Cambridge University Press) · v3. Small corrections. Changed slightly one hypothesis in the definition of the set H of test functions, regarding the decay of the Fourier transform. To appear in Compositio Math
arxiv created 2014/05/05 · openalex publication_date 2014/10/24 · openalex created_date 2016/06/24 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/06
Abstract 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 -functions. In particular, we show how the rank of an elliptic curve over ℚ is encoded in the sequences of zeros of other L -functions, not only the one associated to the curve.