Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms

Atul Dixit, Arindam Roy, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


We generalize a result of Ramanujan, Hardy and Littlewood to the setting of primitive Hecke forms, which interestingly exhibits faster convergence than in the initial case of the Riemann zeta function. We also provide a criterion in the spirit of Riesz for the Riemann Hypothesis for the associated L-functions.

Original languageEnglish (US)
Pages (from-to)594-611
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Jun 1 2015


  • Bessel function
  • Dirichlet series
  • Hecke form
  • Hypergeometric function
  • Möbius function
  • Ramanujan tau function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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