Unnormalized differences between zeros of L-functions

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)230-252
Number of pages23
JournalCompositio Mathematica
Issue number2
StatePublished - Feb 25 2015


  • L-functions
  • Riemann zeta function
  • distribution of zeros

ASJC Scopus subject areas

  • Algebra and Number Theory


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