Double exponential sums over thin sets

John B. Friedlander*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


We estimate double exponential sums of the form Sa(x,y)= ∑x∈x ∑x∈y exp (2πiaxy/p) where is of multiplicative order t modulo the prime p and χ and y are arbitrary subsets of the residue ring modulo t. In the special case t = p-1, our bound is nontrivial for |χ| ≥ |y| ≥ p15/16+δ with any fixed δ > 0, while if in addition we have |χ| ≥ p1-δ/4 it is nontrivial for |y| ≥ p3/4+δ.

Original languageEnglish
Pages (from-to)1617-1621
Number of pages5
JournalProceedings of the American Mathematical Society
Issue number6
Publication statusPublished - 2001


Dive into the research topics of 'Double exponential sums over thin sets'. Together they form a unique fingerprint.

Cite this