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
Let be an integer. Recently, Hu and Lü offered the asymptotic formula for the sum of the higher divisor function where represents the th divisor function. We give the Goldbach-type analogy of their result. That is to say, we investigate the asymptotic behavior of the sum where are prime variables.
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
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).
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.
Sums of Powers of Cusp Form Coefficients. II.
Sums of Products of Certain Arthmetical Functions
Sums of reciprocals of additive functions
Sums of reciprocals of additive functions running over short intervals
Letting f(n) = A log n + t(n), where t(n) is a small additive function and A a positive constant, we obtain estimates for the quantities and , where H = H(x) satisfies certain growth conditions, p runs over prime numbers and Q is a polynomial with integer coefficients, whose leading coefficient is positive, and with all its roots simple.
Sums of some multiplicative functions over a special set of integers