Maximum Stirling numbers of the second kind.
Mean square limit for lattice points in a sphere
Mean square of the remainder term in the Dirichlet divisor problem II
Mean square of the remainder term in the Dirichlet divisor problem
Mean square value of exponential sums related to representation of integers as sum of two squares
Mean square value of exponential sums related to the representation of integers as sums of squares
Mean value estimates for exponential sums and L-functions: a spectral theoretic approach.
Mean value estimates for exponential sums with applications to -functions
Mean Value Estimates in Lattice Point Theory.
Mean Value Properties of the Hurwitz Zeta-Function.
Mean value results for the approximate functional equation of the square of the Riemann zeta-function
Mean value theorems for a class of arithmetic functions
Mean value theorems for binary Egyptian fractions II
Mean value theorems for L-functions over prime polynomials for the rational function field
The first and second moments are established for the family of quadratic Dirichlet L-functions over the rational function field at the central point s=1/2, where the character χ is defined by the Legendre symbol for polynomials over finite fields and runs over all monic irreducible polynomials P of a given odd degree. Asymptotic formulae are derived for fixed finite fields when the degree of P is large. The first moment obtained here is the function field analogue of a result due to Jutila in the...
Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series
We obtain formulas for computing mean values of Dirichlet polynomials that have more terms than the length of the integration range. These formulas allow one to compute the contribution of off-diagonal terms provided one knows the correlation functions for the coefficients of the Dirichlet polynomials. A smooth weight is used to control error terms, and this weight can in typical applications be removed from the final result. Similar results are obtained for the tails of Dirichlet series. Four examples...
Mean values connected with the Dedekind zeta-function of a non-normal cubic field
After Landau’s famous work, many authors contributed to some mean values connected with the Dedekind zetafunction. In this paper, we are interested in the integral power sums of the coefficients of the Dedekind zeta function of a non-normal cubic extension K 3/ℚ, i.e. , where M(m) denotes the number of integral ideals of the field K 3 of norm m and l ∈ ℕ. We improve the previous results for and .
Mean values of a gcd-sum function over regular integers modulo .
Mean values of Dirichlet polynomials and applications to linear equations with prime variables
Mean values of generalized gcd-sum and lcm-sum functions.
Mean values of Hecke L-functions.