Modularity of a certain Calabi-Yau threefold

Scott Ahlgren, Ken Ono

Research output: Contribution to journalArticlepeer-review


The Langlands program predicts that certain Calabi-Yau threefolds are modular in the sense that their L-series correspond to the Mellin transforms of weight 4 newforms. Here we prove that the L-function of the threefold given by ∑4i=1 (xi + x-1i) = 0 is η4(2z)η4(4z), the unique normalized eigenform in S40(8)).

Original languageEnglish (US)
Pages (from-to)129-177
Number of pages49
JournalMonatshefte fur Mathematik
Issue number3
StatePublished - 2000
Externally publishedYes


  • Calabi-yau threefold
  • Modular forms
  • Trace formula

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Modularity of a certain Calabi-Yau threefold'. Together they form a unique fingerprint.

Cite this