Asymptotic expansions of the mean values of DirichletL-functions
نویسندگان
چکیده
منابع مشابه
Asymptotic Expansions of Integral Mean of Polygamma Functions
Let s,t be two given real numbers, s = t and m ∈ N . We determine the coefficients aj(s,t) in the asymptotic expansion of integral (or differential) mean of polygamma functions ψ (m)(x) : 1 t− s ∫ t s ψ (m)(x+u)du ∼ ψ (m) ( x ∞ ∑ j=0 aj(s,t) x j ) , x → ∞. We derive the recursive relations for polynomials aj(t,s) , and also as polynomials in intrinsic variables α = 2 (s + t − 1) , β = 4 [1− (t ...
متن کاملAsymptotic Expansions of Certain Partial Theta Functions
We establish an asymptotic expansion for a class of partial theta functions generalizing a result found in Ramanujan’s second notebook. Properties of the coefficients in this more general asymptotic expansion are studied, with connections made to combinatorics and a certain Dirichlet series.
متن کاملAsymptotic mean values of Gaussian polytopes
We consider geometric functionals of the convex hull of normally distributed random points in Euclidean space R. In particular, we determine the asymptotic behaviour of the expected value of such functionals and of related geometric probabilities, as the number of points increases.
متن کاملMean values of multiplicative functions
Let f(n) be a totally multiplicative function such that |f(n)| ≤ 1 for all n, and let F (s) = ∑∞ n=1 f(n)n−s be the associated Dirichlet series. A variant of Halász’s method is developed, by means of which estimates for ∑N n=1 f(n)/n are obtained in terms of the size of |F (s)| for s near 1 with 1. The result obtained has a number of consequences, particularly concerning the zeros of the p...
متن کاملEUCLIDEAN ASYMPTOTIC EXPANSIONS OF GREEN FUNCTIONS OF QUANTUM FIELDS. (I) Expansions of Products of Singular Functions
The problem of asymptotic expansions of Green functions in perturbative QFT is studied for the class of Euclidean asymptotic regimes. Phenomenological applications are analyzed to obtain a meaningful mathematical formulation of the problem. It is shown that the problem reduces to studying asymptotic expansions of products of a class of singular functions in the sense of the distribution theory....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 1991
ISSN: 0025-5874,1432-1823
DOI: 10.1007/bf02571507