On the transcendence of certain Petersson inner products

Document Type : Special Issue of BIMS in Honor of Professor Freydoon Shahidi



‎We show that for all normalized Hecke eigenforms $f$‎ ‎with weight one and of CM type‎, ‎the number $(f,f)$ where $(\cdot‎, ‎\cdot )$ denotes‎ ‎the Petersson inner product‎, ‎is a linear form in logarithms and‎ ‎hence transcendental‎.


Main Subjects

Volume 43, Issue 4 (Special Issue)
August 2017
Pages 313-316
  • Receive Date: 15 May 2017
  • Revise Date: 01 October 2017
  • Accept Date: 19 May 2017
  • First Publish Date: 30 August 2017