An explicit construction of non-tempered cusp forms on $O(1,8n+1)$ (Analytic and Arithmetic Theory of Automorphic Forms)

IR (HANDLE) Web Site Open Access
  • Li, Yingkun
    Fachbereich Mathematik, Technische Universität Darmstadt
  • Narita, Hiro-aki
    Department of Mathematics, Faculty of Science and Engineering, Waseda University
  • Pitale, Ameya
    Department of Mathematics, University of Oklahoma

Bibliographic Information

Other Title
  • An explicit construction of non-tempered cusp forms on O(1,8n+1)

Search this article

Description

This short note is a write-up of the results presented by the second named author at RIMS workshop "Analytic and arithmetic theory of automorphic forms" The main result is an explicit construction of the rcal analytic cusp forms on O ({imath}, 8n+1) by a lifting from Maass cusp forms of level one. The lifting is proved to be Hecke-equivariant. Our results include an explicit formula for Hecke eigenvalues of the lifts and explicit determination of the cusidal representations generated by them. This leads to showing the nontemperedness of the cuspidal representations at every finite place, namely our explicit construction provides "real analytic counterexamples to Ramanujan conjecture".

Journal

  • RIMS Kokyuroku

    RIMS Kokyuroku 2100 179-186, 2019-01

    京都大学数理解析研究所

Details 詳細情報について

Report a problem

Back to top