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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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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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https://doi.org/10.1007/978-3-663-07645-2on to the Hasse principle and no . Brauer–Manin obstruction. In this paper, we show that the nontrivial Brauer class of . does not descend to .. Together with the results of Várilly-Alvarado and Viray (Adv. Math. 226(6):4884–4901, 2011), this proves that the Brauer–Manin obstruction is insufficient
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Germanischer Bereich, Deutschlandthe 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 the splitting field of the polynomial .. If . satisfies Va
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Germanischer Bereich, Deutschlandgroup 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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Christina Simon-Philipp,Gerd Kuhnple 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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Die Nachkriegsära und ihre Leitbilderances of PLWE. In: Proceedings of the selected areas of cryptography 2014. Lecture notes in computer science. Springer, New York, 2014; Elias Y., Lauter K., Ozman E., Stange K., Provably weak instances of ring-LWE. In: Advances in Cryptology – CRYPTO 2015. Springer, 2015 gives rise to interesting qu
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Christa Reicher,Anne Söfker-Rienietsat 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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Directions in Number Theory978-3-319-30976-7Series ISSN 2364-5733 Series E-ISSN 2364-5741
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