On the third moment of L (1 2, χd) II: The number field case

Adrian Diaconu, Ian Whitehead

Research output: Contribution to journalArticlepeer-review


We establish a smoothed asymptotic formula for the third moment of quadratic Dirichlet L-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size x3=4. The error term in the asymptotic formula is on the order of O(x2=3+δ) for every δ > 0:

Original languageEnglish (US)
Pages (from-to)2051-2070
Number of pages20
JournalJournal of the European Mathematical Society
Issue number6
StatePublished - Feb 24 2021

Bibliographical note

Publisher Copyright:
© 2021 European Mathematical Society.


  • Cubic moment
  • Quadratic Dirichlet L-functions
  • Smoothed asymptotic formula
  • Weyl group multiple Dirichlet series


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