Automorphic forms for some even unimodular lattices

  title={Automorphic forms for some even unimodular lattices},
  author={Neil Dummigan and Dan Fretwell},
  journal={Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg},
  • N. Dummigan, D. Fretwell
  • Published 19 March 2020
  • Mathematics
  • Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
We look at genera of even unimodular lattices of rank 12 over the ring of integers of $${{\mathbb {Q}}}(\sqrt{5})$$ Q ( 5 ) and of rank 8 over the ring of integers of $${{\mathbb {Q}}}(\sqrt{3})$$ Q ( 3 ) , using Kneser neighbours to diagonalise spaces of scalar-valued algebraic modular forms. We conjecture most of the global Arthur parameters, and prove several of them using theta series, in the manner of Ikeda and Yamana. We find instances of congruences for non-parallel weight Hilbert… 
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