دورية أكاديمية
The Riemann zeta in terms of the dilogarithm
| العنوان: | The Riemann zeta in terms of the dilogarithm |
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| المؤلفون: | Albeverio, S., CACCIAPUOTI, CLAUDIO |
| المساهمون: | Albeverio, S., Cacciapuoti, Claudio |
| سنة النشر: | 2013 |
| المجموعة: | IRInSubria - Institutional Repository Insubria (Università degli Studi dell’Insubria) |
| مصطلحات موضوعية: | 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 function, Series of zeta function, Zero-free regions of the zeta function |
| الوصف: | We give a representation of the classical Riemann ζ-function in the half plane Res > 0 in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen Gl2-function). We also derive corresponding representations involving the derivatives of the Gl2-function. A generalized symmetrized Müntz-type formula is also derived. For a special choice of test functions it connects to our integral representation of the ζ-function, providing also a computation of a concrete Mellin transform. Certain formulae involving series of zeta functions and gamma functions are also derived. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| العلاقة: | info:eu-repo/semantics/altIdentifier/wos/WOS:000310182600019; volume:133; issue:1; firstpage:242; lastpage:277; numberofpages:36; journal:JOURNAL OF NUMBER THEORY; http://hdl.handle.net/11383/1926121Test; info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-84867305642 |
| DOI: | 10.1016/j.jnt.2012.06.002 |
| الإتاحة: | https://doi.org/10.1016/j.jnt.2012.06.002Test http://hdl.handle.net/11383/1926121Test |
| رقم الانضمام: | edsbas.14F902 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1016/j.jnt.2012.06.002 |
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