Summatory function of the Möbius function. II: Elementary asymptotic upper bounds. (Fonction sommatoire de la fonction de Möbius. II: Majorations asymptotiques élémentaires.)
Sums and differences of additive arithmetic functions in mean square.
Sums and differences of power-free numbers
We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions a, b ∈ ℕ to the equations a + b = n and a - b = n, where a is k-free and b is l-free. This is the first time that this problem has been studied with distinct powers k and l.
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
Sums of squares in
Sums of the additive divisor problem type and the inner product method.
Sums of the divisor and unitary divisor functions.
Sums of two relatively prime cubes