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Titlebook: Directions in Number Theory; Proceedings of the 2 Ellen E. Eischen,Ling Long,Katherine E. Stange Conference proceedings 2016 The Editor(s)

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书目名称Directions in Number Theory
副标题Proceedings of the 2
编辑Ellen E. Eischen,Ling Long,Katherine E. Stange
视频video
概述Includes papers spanning a wide range of research areas, including arithmetic geometry, analytic number theory, algebraic number theory, and applications to coding and cryptography.Features the contri
丛书名称Association for Women in Mathematics Series
图书封面Titlebook: Directions in Number Theory; Proceedings of the 2 Ellen E. Eischen,Ling Long,Katherine E. Stange Conference proceedings 2016 The Editor(s)
描述Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014. The papers span a wide range of research areas: arithmetic geometry; analytic number theory; algebraic number theory; and applications to coding and cryptography..The WIN conference series began in 2008, with the aim of strengthening the research careers of female number theorists. The series introduced a novel research-mentorship model: women at all career stages, from graduate students to senior members of the community, joined forces to work in focused research groups on cutting-edge projects designed and led by experienced researchers. The goals for Women In Numbers 3 were to establish ambitious new collaborations between women in number theory, to train junior participants about topics of current importance, and to continue to build a vibrant community of women in number theory. Forty-two women attend
出版日期Conference proceedings 2016
关键词Arithmetic Geometry; Elliptic Curves; Galois Theory; arithmetic of curves; Shimura curves; analytic numbe
版次1
doihttps://doi.org/10.1007/978-3-319-30976-7
isbn_softcover978-3-319-80934-2
isbn_ebook978-3-319-30976-7Series ISSN 2364-5733 Series E-ISSN 2364-5741
issn_series 2364-5733
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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Shadow Lines in the Arithmetic of Elliptic Curves,for . we have a corresponding line in ., known as a shadow line. When . has analytic rank 2 and .∕. has analytic rank 3, shadow lines are expected to lie in .. If, in addition, . splits in ., then shadow lines can be determined using the anticyclotomic .-adic height pairing. We develop an algorithm
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,Zeta Functions of a Class of Artin–Schreier Curves with Many Automorphisms,group of these curves contains a large extraspecial group as a subgroup. Precise knowledge of this subgroup makes it possible to compute the zeta function of the curves in this class over the field of definition of all automorphisms in the subgroup.
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,-Adic ,-Expansion Principles on Unitary Shimura Varieties,ple for .-adic modular forms on the Igusa tower says that if the coefficients of (sufficiently many of) the .-expansions of a .-adic modular form . are zero, then . vanishes everywhere on the Igusa tower. There is no .-adic .-expansion principle for unitary groups of arbitrary signature in the liter
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Asymptotics for Number Fields and Class Groups,at readers new to the area. Instead of a thorough treatment of the most general cases, it treats the simplest cases in detailed way, with an emphasis on connections and perspectives that are well known to experts but absent from the literature.
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2364-5733 new collaborations between women in number theory, to train junior participants about topics of current importance, and to continue to build a vibrant community of women in number theory. Forty-two women attend978-3-319-80934-2978-3-319-30976-7Series ISSN 2364-5733 Series E-ISSN 2364-5741
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Galois Action on the Homology of Fermat Curves,2):501 – 561, 1987), the author determines the homology of the degree . Fermat curve as a Galois module for the action of the absolute Galois group .. In particular, when . is an odd prime ., he shows that the action of . on a more powerful relative homology group factors through the Galois group of
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