Investigating the exceptionality of scattered polynomials

Scattered polynomials over a finite field F q n have been introduced by Sheekey in 2016, and central open problem regards the classification of those that are exceptional . So far, only two families scattered known. Very recently, Longobardi Zanella weakened property being introducing notion L- t -partially R- polynomials, for divisor Indeed, polynomial is if it both scattered. In this paper, using techniques from algebraic geometry fields function theory, we show which hardest to be preserved one. We investigate large family containing examples turn out connected with linear sets so-called pseudoregulus type introduce different notions equivalence preserving Many inequivalent geometric arguments used determine their classes under action ? L ( 2 / , )