この論文をさがす
説明
We give a representation of the classical Riemann $��$-function in the half plane $\Re s>0$ in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen $Gl_2$-function). We also derive corresponding representations involving the derivatives of the $Gl_2$-function. A generalized symmetrized M��ntz-type formula is also derived. For a special choice of test functions it connects to our integral representation of the $��$-function, providing also a computation of a concrete Mellin transform. Certain formulae involving series of zeta functions and gamma functions are also derived.
revised version, major changes in Sec. 3 and 5, 25 pages
収録刊行物
-
- Journal of Number Theory
-
Journal of Number Theory 133 242-277, 2013-01-01
Elsevier BV
- Tweet
キーワード
- Generalized symmetrized Müntz formula
- Algebra and Number Theory
- Mathematics - Number Theory
- Dilogarithm function
- Integral representations of the zeta function
- Classical Riemannʼs zeta function
- Meromorphic character of ζ
- Series of zeta functions
- Series of gamma functions
- FOS: Mathematics
- 11M26, 11M06, 11F27 (Primary) 42A38 (Secondary)
- Bounds on the zeta function; Classical Riemann's zeta function; Dilogarithm function; Generalized symmetrized Müntz formula; Integral representations of the zeta function; Mellin transform; Meromorphic character of ζ; Series of gamma functions; Series of zeta functions; Zero-free regions of the zeta function
- Number Theory (math.NT)
- Bounds on the zeta function
- Mellin transform
- Zero-free regions of the zeta function
詳細情報 詳細情報について
-
- CRID
- 1871709542909824896
-
- HANDLE
- 11383/1926121
-
- ISSN
- 0022314X
-
- データソース種別
-
- OpenAIRE