By Jörg Arndt,Christoph Haenel
By Jörg Arndt,Christoph Haenel
By Jianqiang Zhao
This is the 1st introductory e-book on a number of zeta capabilities and a number of polylogarithms that are the generalizations of the Riemann zeta functionality and the classical polylogarithms, respectively, to the a number of variable atmosphere. It includes all of the easy techniques and the $64000 houses of those capabilities and their unique values. This e-book is aimed toward graduate scholars, mathematicians and physicists who're attracted to this present energetic quarter of research.
The ebook will supply a close and finished creation to those items, their attention-grabbing homes and fascinating kinfolk to different mathematical topics, and numerous generalizations resembling their q-analogs and their finite types (by taking partial sums modulo appropriate leading powers). historic notes and routines are supplied on the finish of every chapter.
By Pierre Cartier,Luc Illusie,Nicholas M. Katz,Gérard Laumon,Yuri I. Manin,Kenneth A. Ribet
This three-volume paintings comprises articles accrued at the social gathering of Alexander Grothendieck’s 60th birthday and initially released in 1990. The articles have been provided as a tribute to 1 of the world’s maximum residing mathematicians. some of the groundbreaking contributions in those volumes include fabric that's now thought of foundational to the topic. themes addressed through those top-notch participants fit the breadth of Grothendieck’s personal pursuits, together with: useful research, algebraic geometry, algebraic topology, quantity conception, illustration idea, K-theory, type concept, and homological algebra.
By John Wallis,Jacqueline A. Stedall
John Wallis (1616-1703) used to be the most influential English mathematician sooner than Newton. He released his most famed paintings, Arithmetica Infinitorum, in Latin in 1656. This publication studied the quadrature of curves and systematised the research of Descartes and Cavelieri. Upon e-book, this article instantly turned the traditional ebook at the topic and was once often pointed out through next writers. this can be the 1st English translation of this article ever to be published.
By Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
This ebook positive aspects contemporary advancements in a speedily growing to be zone on the interface of higher-dimensional birational geometry and mathematics geometry. It specializes in the geometry of areas of rational curves, with an emphasis on purposes to mathematics questions. Classically, mathematics is the research of rational or essential ideas of diophantine equations and geometry is the learn of strains and conics. From the trendy point of view, mathematics is the learn of rational and vital issues on algebraic forms over nonclosed fields. an important perception of the 20 th century was once that mathematics houses of an algebraic style are tightly associated with the geometry of rational curves at the kind and the way they range in families.
This choice of solicited survey and examine papers is meant to function an creation for graduate scholars and researchers attracted to coming into the sector, and as a resource of reference for specialists engaged on comparable difficulties. subject matters that may be addressed comprise: birational houses akin to rationality, unirationality, and rational connectedness, lifestyles of rational curves in prescribed homology periods, cones of rational curves on rationally hooked up and Calabi-Yau forms, in addition to comparable questions in the framework of the minimum version Program.
By Michel Lapidus,Machiel van Frankenhuijsen
Number conception, spectral geometry, and fractal geometry are interlinked during this in-depth examine of the vibrations of fractal strings, that's, one-dimensional drums with fractal boundary.
Throughout Geometry, advanced Dimensions and Zeta features, Second Edition, new effects are tested and a new definition of fractality because the presence of nonreal advanced dimensions with optimistic genuine components is gifted. The new final chapter discusses numerous new subject matters and effects got because the e-book of the 1st edition.
By Manfred Einsiedler
By Haruzo Hida
By Jörn Steuding
These notes current fresh leads to the value-distribution thought of L-functions with emphasis at the phenomenon of universality. Universality has a powerful influence at the zero-distribution: Riemann’s speculation is right provided that the Riemann zeta-function can approximate itself uniformly. The textual content proves universality for polynomial Euler items. The authors’ method follows in most cases Bagchi's probabilistic approach. dialogue touches on similar issues: nearly periodicity, density estimates, Nevanlinna concept, and useful independence.
By Natanael Méndez Matos