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Let $l ⩾ 2$ be an integer. Recently, Hu and Lü offered the asymptotic formula for the sum of the higher divisor function $\sum_{1 ⩽ n_{1}, n_{2}, ..., n_{l} ⩽ x^{1 / 2}} τ_{k} (n_{1}^{2} + n_{2}^{2} + \dots + n_{l}^{2}),$ where $τ_{k} (n)$ represents the $k$ th divisor function. We give the Goldbach-type analogy of their result. That is to say, we investigate the asymptotic behavior of the sum $\sum_{1 ⩽ p_{1}, p_{2}, ..., p_{l} ⩽ x} τ_{k} (p_{1} + p_{2} + \dots + p_{l}),$ where $p_{1}, p_{2}, \dots, p_{l}$ are prime variables.

We find, via the Selberg-Delange method, an asymptotic formula for the mean of arithmetic functions on certain APs. It generalizes a result due to Cui and Wu (2014).

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Some $Ω$ -results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem

Sommes de carrés de polynômes irréductibles dans $F_{q} [X]$

Sommes de diviseurs et structure multiplicative des entiers

Sommes de Reciproques de Grandes Fonctions Additives

Sommes d'exponentielles et principe de l'hyperbole

Square free values of the order function.

Square-full divisors of square-full integers.

Still another proof of Parseval's equation for almost-even arithmetical functions.

Subconvexity for the Riemann zeta-function and the divisor problem

Sum of higher divisor function with prime summands

Summation operators and "explicit formulas"

Sums and differences of additive arithmetic functions in mean square.

Sums involving the largest prime divisor of an integer

Sums of additive functions on arithmetical semigroups

Sums of arithmetic functions over values of binary forms

Sums of multiplicative function in special arithmetic progressions

Sums of nonnegative multiplicative functions over integers without large prime factors II

Sums of nonnegative multiplicative functions over integers without large prime factors I

Sums of Periodicals of Certain Additive Functions.

Sums of Powers of Cusp Form Coefficients.

Currently displaying 501 – 520 of 715