Nair–Tenenbaum bounds uniform with respect to the discriminant

Abstract

Abstract For functions F satisfying a certain submultiplicativity condition and polynomials Q 1 , . . ., Q k in [ X ], Nair and Tenenbaum obtained an upper bound on the short sum $\sum_{x < n \leq x+y} F(|Q_{1}(n)|,\dotsc,|Q_{k}(n)|)$ with an implicit dependency on the discriminant of Q 1 . . . Q k . We obtain a similar upper bound uniform in the discriminant.

Locations

• Mathematical Proceedings of the Cambridge Philosophical Society - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View