Discrete limit theorems for the Mellin transform of the Riemann zeta-function
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...
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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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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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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2008
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa131-1-2