On the maximal order in $S_n$ and $S*_n$

M. Szalay

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A simple elementary proof of $M (x) = \sum_{n \leq x} μ (n) = o (x)$

M. Kalecki (1967)

Acta Arithmetica

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On some estimates involving the number of prime divisors of an integer

Aleksandar Ivić (1987)

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On the error term in the linear sieve

Henryk Iwaniec (1971)

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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 $Ψ (x, y) = |\{n \leq x : p ∣ n \Rightarrow p \leq y\}|$ with a very good error term, valid for $exp ({(log log x)}^{(5 / 3) + ϵ}) \leq y \leq x$ , $x \geq x_{0} (ϵ)$ , $ϵ > 0 .$ 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.

Some asymptotic formulas on generalized divisor functions, III

András Sárközy, P. Erdös (1982)

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New bounds on the number of representation of $t$ as a binomial coefficient.

Kane, Daniel (2004)

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Normal order for divisor functions of generalized integers

Horadam, E.M. (1968)

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On the maximal distance between integers composed of small primes

R. Tijdeman (1974)

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Displaying similar documents to “On the maximal order in S n and S * n ”

Displaying similar documents to “On the maximal order in $S_{n}$ and $S *_{n}$ ”