On additive representation functions

R. Balasubramanian, Sumit Giri

Research output: Contribution to journalArticlepeer-review


Let = {a1 < a2 < a3 < ⋯ < an < ⋯} be an infinite sequence of nonnegative integers and let R2(n) = |{(i, j): ai + aj = n; ai, aj ; i ≤ j}|. We define Sk = ∑l = 1k(R2(2l)-R2(2l + 1)). We prove that if the L-norm of Sk+(= max Sk, 0) is small, then the L1-norm of 1/4Sk+k is large.

Original languageEnglish
Pages (from-to)1165-1176
Number of pages12
JournalInternational Journal of Number Theory
Issue number4
StatePublished - 5 Jun 2015
Externally publishedYes


  • Additive representation functions
  • Sidon set
  • general sequence
  • monotonicity


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