Exponential and character sums with mersenne numbers

William D. Banks, John B. Friedlander, Moubariz Z. Garaev, Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
16 Downloads (Pure)


We give new bounds on sums of the form Σ n≤N ∧ (n) exp (2πiag n/m) and Σ n≤N ∧ (n)Χ(g n + a), where ∧ is the von Mangoldt function, m is a natural number, a and g are integers coprime to m, and Χ is a multiplicative character modulom. In particular, our results yield bounds on the sums Σ p≤N exp (2πiaM p/m) and Σ p≤N Χ(M p) with Mersenne numbers M p = 2 p - 1, where p is prime.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalJournal of the Australian Mathematical Society
Issue number1
Publication statusPublished - Feb 2012


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