Displaying similar documents to “The complex sum of digits function and primes”

On the almost Goldbach problem of Linnik

Jianya Liu, Ming-Chit Liu, Tianze Wang (1999)

Journal de théorie des nombres de Bordeaux

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Under the Generalized Riemann Hypothesis, it is proved that for any k ≥ 200 there is N k > 0 depending on k only such that every even integer ≥ N k is a sum of two odd primes and k powers of 2 .

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.

On the largest prime factor of n ! + 2 n - 1

Florian Luca, Igor E. Shparlinski (2005)

Journal de Théorie des Nombres de Bordeaux

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For an integer n ≥ 2 we denote by P ( n ) the largest prime factor of n . We obtain several upper bounds on the number of solutions of congruences of the form n ! + 2 n - 1 ≡ 0 ( mod q ) and use these bounds to show that lim sup n → ∞ P ( n ! + 2 n - 1 ) / n ≥ ( 2 π 2 + 3 ) / 18 .

P 2 in short intervals

Henryk Iwaniec, M. Laborde (1981)

Annales de l'institut Fourier

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For any sufficiently large real number x , the interval [ x , x + x 0 , 45 ] contains at least one integer having at most two prime factors .