| 書目名稱 | Pseudodifferential Methods in Number Theory | | 編輯 | André Unterberger | | 視頻video | http://file.papertrans.cn/763/762525/762525.mp4 | | 概述 | Explores a new approach to the Riemann hypothesis.Explains the link between the theory of modular distributions and the classical one of modular forms.Includes previously unpublished material | | 叢書名稱 | Pseudo-Differential Operators | | 圖書封面 |  | | 描述 | .Classically developed as a tool for partial differential equations, the?analysis of operators known as pseudodifferential analysis is here regarded?as a possible help in questions of arithmetic. The operators which make up?the main subject of the book can be characterized in terms of congruence?arithmetic.?They enjoy a Eulerian structure, and are applied to the search?for new conditions equivalent to the Riemann hypothesis. These consist in?the validity of certain parameter-dependent estimates for a class of Hermitian?forms of finite rank. The Littlewood criterion, involving sums of?M?bius coefficients, and the Weil so-called explicit formula, which leads to?his positivity criterion, fit within this scheme, using in the first case Weyl‘s?pseudodifferential calculus, in the second case Fuchs‘.?.The book should be?of interest to people looking for new possible approaches to the Riemann?hypothesis, also to newperspectives on pseudodifferential analysis and on?the way it combines with modular form theory. Analysts will have no difficulty with the arithmetic aspects, with which, save for very few exceptions,?no previous acquaintance is necessary.. | | 出版日期 | Book 2018 | | 關(guān)鍵詞 | pseudodifferential analysis in arithmetic; approach to the zeros of Riemann‘s zeta function; modular d | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-92707-7 | | isbn_softcover | 978-3-319-92706-0 | | isbn_ebook | 978-3-319-92707-7Series ISSN 2297-0355 Series E-ISSN 2297-0363 | | issn_series | 2297-0355 | | copyright | Springer Nature Switzerland AG 2018 |
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