Displaying 121 – 140 of 498

Showing per page

On ideals free of large prime factors

Eira J. Scourfield (2004)

Journal de Théorie des Nombres de Bordeaux

In 1989, E. Saias established an asymptotic formula for Ψ ( x , y ) = n x : p n p y with a very good error term, valid for exp ( log log x ) ( 5 / 3 ) + ϵ y x , x x 0 ( ϵ ) , ϵ > 0 . We extend this result to an algebraic number field K by obtaining an asymptotic formula for the analogous function Ψ K ( x , y ) with the same error term and valid in the same region. Our main objective is to compare the formulae for Ψ ( x , y ) and Ψ K ( x , y ) , and in particular to compare the second term in the two expansions.

Currently displaying 121 – 140 of 498