Two-parameter identities for divisor sums in algebraic number fields

Bruce C. Berndt, Martino Fassina, Sun Kim, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


In a one-page fragment published with his lost notebook, Ramanujan stated two double series identities associated, respectively, with the famous Gauss Circle and Dirichlet Divisor problems. The identities contain an “extra” parameter, and it is possible that Ramanujan derived these identities with the intent of attacking these famous problems. Similar famous unsolved problems are connected with fK(n), the number of integral ideals of norm n in an algebraic number field K. In this paper we establish Riesz sum identities containing an “extra” parameter and involving fK(n), or divisor functions associated with K. Upper bounds for the sums as the upper index tends to infinity are also established.

Original languageEnglish (US)
Article number125679
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - Feb 15 2022


  • Bessel functions
  • Dedekind zeta function
  • Dirichlet character
  • Dirichlet divisor problem
  • Ideal functions
  • Ramanujan's lost notebook

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


Dive into the research topics of 'Two-parameter identities for divisor sums in algebraic number fields'. Together they form a unique fingerprint.

Cite this