Normal Algebraic Number Fields [PDF]
Proceedings of the National Academy of Sciences, 1940 MacLane, Saunders, Schilling, O. F. G.
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The Genus Field and Genus Number in Algebraic Number Fields [PDF]
Nagoya Mathematical Journal, 1967 Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.
Yoshiomi Furuta
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Congruence representations in algebraic number fields [PDF]
Transactions of the American Mathematical Society, 1953 Eckford Cohen
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Constructions of Dense Lattices over Number Fields
Trends in Computational and Applied Mathematics, 2020 In this work, we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2,3,4,5,6,8 and 12, which are rotated versions of the lattices Lambda_n, for n =2,3,4,5,6,8 and K_12.
Antonio A. Andrade +3 more
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Quartic surfaces, their bitangents and rational points [PDF]
Épijournal de Géométrie Algébrique, 2023 Let X be a smooth quartic surface not containing lines, defined over a number field K. We prove that there are only finitely many bitangents to X which are defined over K.
Pietro Corvaja, Francesco Zucconi
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The Impact of Mental Computation on Children’s Mathematical Communication, Problem Solving, Reasoning, and Algebraic Thinking [PDF]
Athens Journal of Education, 2020 Moving from arithmetic to algebraic thinking at early grades is foundational in the study of number patterns and number relationships. This qualitative study investigates mental computational activity in a third grade classroom’s and its relationship to ...
Roland Pourdavood +2 more
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Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination [PDF]
Logical Methods in Computer Science, 2012 This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties.
Assia Mahboubi, Cyril Cohen
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Lower bounds on the class number of algebraic function fields defined over any finite field [PDF]
, 2011 We give lower bounds on the number of effective divisors of degree $\leq g-1$ with respect to the number of places of certain degrees of an algebraic function field of genus $g$ defined over a finite field.
Ballet, Stéphane, Rolland, Robert
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A Construction of Rotated Lattices via Totally Real Subfields of the Cyclotomic Field Q(z_p)
Trends in Computational and Applied Mathematics, 2019 The theory of lattices have shown to be useful in information theory and rotated lattices with high modulations diversity have been extensively studied as an alternative approach for transmission over a Rayleigh-fading channel, where the performance of ...
Antonio A. Andrade +2 more
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Arithmetic of Calabi-Yau Varieties and Rational Conformal Field Theory [PDF]
, 2001 It is proposed that certain techniques from arithmetic algebraic geometry provide a framework which is useful to formulate a direct and intrinsic link between the geometry of Calabi-Yau manifolds and the underlying conformal field theory. Specifically it
Candelas +16 more
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