Erratum to: “The Mellin Transform of Hardy’s Function is Entire”
نویسندگان
چکیده
منابع مشابه
Mellin transform techniques for zeta-function resummations
Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the result is naturally split into the same three contributions of very different nature, i.e. the series of Riemann zeta functions and the power and negative e...
متن کاملThe Mellin transform of the square of Riemann's zeta-function
This function, when k = 2, was introduced by Y. Motohashi [15] (see also [16]), and its properties were further studied in [10] and [11]. The latter work also contains some results on the function Z1(s), which is the principal object of the study in this paper. It was shown that Z1(s) is regular for σ > −3/4, except for a double pole at s = 1. The principal part of the Laurent expansion of Z1(s...
متن کاملThe Mellin transform of the square of Riemann’s zeta-function
This function, when k = 2, was introduced by Y. Motohashi [15] (see also [16]), and its properties were further studied in [10] and [11]. The latter work also contains some results on the function Z1(s), which is the principal object of the study in this paper. It was shown that Z1(s) is regular for σ > −3/4, except for a double pole at s = 1. The principal part of the Laurent expansion of Z1(s...
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The modified Mellin transform Zk(s) = ∫ ∞ 1 |ζ( 1 2 + ix)|x dx (k ∈ N) is investigated. Analytic continuation and mean square estimates of Zk(s) are discussed, as well as connections with power moments of |ζ( 1 2 +ix)|, with the special emphasis on the cases k = 1, 2.
متن کاملThe Twisted Mellin Transform
The “twisted Mellin transform” is a slightly modified version of the usual classical Mellin transform on L([0,∞)). In this short note we investigate some of its basic properties. From the point of view of combinatorics one of its most interesting properties is that it intertwines the differential operator, df/dx, with its finite difference analogue, ∇f = f(x)−f(x−1). From the point of view of a...
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ژورنال
عنوان ژورنال: Mathematical Notes
سال: 2010
ISSN: 0001-4346,1573-8876
DOI: 10.1134/s0001434610110167