Number theory. Transl. from the 3rd German edition, edited and with a preface by Horst Günter Zimmer.

zbMath0991.11001MaRDI QIDQ5957128

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Publication date: 6 March 2002

Published in: Classics in Mathematics (Search for Journal in Brave)

zbMATH Keywords

function fieldsdivisornumber fieldsvaluationsclass groupdifferentdiscriminantunit group

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01) Algebraic number theory: global fields (11Rxx) Non-Archimedean valued fields (12J25) Valued fields (12J10) General valuation theory for fields (12J20) Algebraic number theory: local fields (11Sxx)

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Irreducibility of generalized Hermite-Laguerre polynomials. III. ⋮ On the cohomological dimension of pro-\(p\)-extensions of number fields ⋮ Explicit integral Galois module structure of weakly ramified extensions of local fields ⋮ On wild ramification in quaternion extensions ⋮ EISENSTEIN POLYNOMIALS DEFINING CYCLIC p-ADIC FIELDS WITH MINIMAL WILD RAMIFICATION ⋮ Representing algebraic integers as linear combinations of units ⋮ Irreducibility of generalized Laguerre polynomials \(L_n^{(\frac{1}{2} + u)}(x)\) with integer \(u\) ⋮ On the sharpness of the bound for the Local Converse Theorem of 𝑝-adic 𝐺𝐿_{𝑝𝑟𝑖𝑚𝑒} ⋮ Siegel fields ⋮ Absolute norms of \(p\)-primary units ⋮ Dirichlet series associated to quartic fields with given cubic resolvent ⋮ Irreducibility of extensions of Laguerre polynomials

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