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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,Insufficiency of the Brauer–Manin Obstruction for Rational Points on Enriques Surfaces,ne, Preprint): we study geometrically unramified Brauer classes on . via pullback of ramified Brauer classes on a rational surface. Notably, we develop techniques which work over fields which are not necessarily separably closed, in particular, over number fields.

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,Städtische Atmosphäre und Stadtklima,In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of “hypergeometric” algebraic varieties that are higher dimensional analogues of Legendre curves.

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Hypergeometric Series, Truncated Hypergeometric Series, and Gaussian Hypergeometric Functions,In this paper, we investigate the relationships among hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions through some families of “hypergeometric” algebraic varieties that are higher dimensional analogues of Legendre curves.

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Ellen E. Eischen,Ling Long,Katherine E. StangeIncludes 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

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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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