Subconvexity for modular form L-functions in the t aspect

Andrew R. Booker*, Micah B. Milinovich, Nathan Ng

*Corresponding author for this work

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

6 Citations (Scopus)
97 Downloads (Pure)


Modifying a method of Jutila, we prove a t-aspect subconvexity estimate for L-functions associated to primitive holomorphic cusp forms of arbitrary level that is of comparable strength to Good's bound for the full modular group, thus improving on a 36-year-old result. A key innovation in our proof is a general form of Voronoi summation that applies to all fractions, even when the level is not squarefree.
Original languageEnglish
Pages (from-to)299-335
Number of pages37
JournalAdvances in Mathematics
Early online date1 Nov 2018
Publication statusPublished - 7 Jan 2019


  • Subconvexity
  • Modular forms
  • L-functions


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