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Displaying 461 – 480 of 498

On the spinor zeta functions problem: higher power moments of the Riesz mean

Haiyan Wang (2013)

Acta Arithmetica

Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp₂(ℤ) of genus 2. The coefficients of the spinor zeta function $Z_{F} (s)$ are denoted by cₙ. Let $D_{ρ} (x; Z_{F})$ be the Riesz mean of cₙ. Kohnen and Wang obtained the truncated Voronoï-type formula for $D_{ρ} (x; Z_{F})$ under the Ramanujan-Petersson conjecture. In this paper, we study the higher power moments of $D_{ρ} (x; Z_{F})$ , and then derive an asymptotic formula for the hth (h=3,4,5) power moments of $D ₁ (x; Z_{F})$ by using Ivić’s large value arguments and other techniques.

On the square-free sieve

H. A. Helfgott (2004)

Acta Arithmetica

On the sum ... D(n) ... (n + N).

U. Balakrishnan, J. Sengupta (1990)

Manuscripta mathematica

On the sum of iterations of the Euler function.

Shparlinski, Igor E. (2006)

Journal of Integer Sequences [electronic only]

On the sum of the first n values of the Euler function

R. Balasubramanian, Florian Luca, Dimbinaina Ralaivaosaona (2014)

Acta Arithmetica

Let ϕ(n) be the Euler function of n. We put $E (n) = \sum_{m \leq n} ϕ (m) - (3 / π ²) n ²$ and give an asymptotic formula for the second moment of E(n).

On the sum of the number of divisors in a short segment

Yoichi Motohashi (1970)

Acta Arithmetica

On the Sum-of-Divisors Function of the Numbers of Fermat and Ferentinou-Nicolacopoulou

Florian Luca (2002)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On the switching principle in sieve theory.

E. Fouvry, F. Grupp (1986)

Journal für die reine und angewandte Mathematik

On the symmetry of divisor sums functions in almost all short intervals.

Coppola, G. (2004)

Integers

On the symmetry of square-free supported arithmetical functions in short intervals.

Coppola, Giovanni (2004)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On the symmetry of the divisor function in almost all short intervals

G. Coppola, S. Salerno (2004)

Acta Arithmetica

On the tails of the limiting distribution function of the error term in the Dirichlet divisor problem

Yuk-Kam Lau (2001)

Acta Arithmetica

On the Tauberian constant in the Ikehara theorem

Jiří Čížek (1999)

Czechoslovak Mathematical Journal

On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus

Karin Halupczok (2009)

Journal de Théorie des Nombres de Bordeaux

For $ε > 0$ and any sufficiently large odd $n$ we show that for almost all $k \leq R : = n^{1 / 5 - ε}$ there exists a representation $n = p_{1} + p_{2} + p_{3}$ with primes $p_{i} \equiv b_{i}$ mod $k$ for almost all admissible triplets $b_{1}, b_{2}, b_{3}$ of reduced residues mod $k$ .

On the third iterates of the φ- and σ-functions

H. Maier (1984)

Colloquium Mathematicae

On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers

R. Stoneham (1973)

Acta Arithmetica

On the unimodal character of the frequency function of the largest prime factor

Jean-Marie De Koninck, Jason Pierre Sweeney (2001)

Colloquium Mathematicae

The main objective of this paper is to analyze the unimodal character of the frequency function of the largest prime factor. To do that, let P(n) stand for the largest prime factor of n. Then define f(x,p): = #{n ≤ x | P(n) = p}. If f(x,p) is considered as a function of p, for 2 ≤ p ≤ x, the primes in the interval [2,x] belong to three intervals I₁(x) = [2,v(x)], I₂(x) = ]v(x),w(x)[ and I₃(x) = [w(x),x], with v(x) < w(x), such that f(x,p) increases for p ∈ I₁(x), reaches its maximum value in...

On the upper bound for π₂(x)

Yingchun Cai, Minggao Lu (2003)

Acta Arithmetica

On the value distribution of a class of arithmetic functions

Werner Georg Nowak (1996)

Commentationes Mathematicae Universitatis Carolinae

This article deals with the value distribution of multiplicative prime-independent arithmetic functions $(α (n))$ with $α (n) = 1$ if $n$ is $N$ -free ( $N \geq 2$ a fixed integer), $α (n) > 1$ else, and $α (2^{n}) \to \infty$ . An asymptotic result is established with an error term probably definitive on the basis of the present knowledge about the zeros of the zeta-function. Applications to the enumerative functions of Abelian groups and of semisimple rings of given finite order are discussed.

On the values of Euler's φ-function

P. Erdös, R. Hall (1973)

Acta Arithmetica

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