Displaying similar documents to “Some Ω-theorems for the Riemann zeta-function”

On ideals free of large prime factors

Eira J. Scourfield (2004)

Journal de Théorie des Nombres de Bordeaux

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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.