Multi-target hyperbolic sieves and elliptic trace obstructions

Pantelimon Stănică, Erik Mulder, Markus Hittmeir

Let $N=pq$ be a semiprime and let $\ell \nmid Na$ be an odd prime. The hyperbolic sieve set $H_a(N;\ell )=\{ax+N{x}^{-1}:x\in {\mathbb{F}}_{\ell }^{\ast }\}$ contains the residue of the linear form…