Large values of newforms on GL(2) with highly ramified central character

Abhishek Saha

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)
277 Downloads (Pure)


We give a lower bound for the sup-norm of an L2-normalized newform in an irreducible, unitary, cuspidal representation of π of GL2 over a number field. When the central character of ππ is sufficiently ramified, this bound improves upon the trivial bound by a positive power of N,, where N is the norm of the conductor of π. This generalizes a result of Templier, who dealt with the special case when the conductor of the central character equals the conductor of the representation. We also make a conjecture about the true size of the sup-norm in the N-aspect that takes into account this central character phenomenon. Our results depend upon some explicit formulas and bounds for the Whittaker newvector over a non-archimedean local field, which may be of independent interest.
Original languageEnglish
Pages (from-to)4103-4131
JournalInternational Mathematics Research Notices
Issue number13
Early online date1 Oct 2015
Publication statusPublished - 1 Oct 2015


  • math.NT


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