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Algebraic Number Theory and Code Design for Rayleigh Fading Channels [PDF]
Foundations and Trends in Communications and Information Theory, 2004 Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems.
Frédérique Oggier, Emanuele Viterbo
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Rooting out letters: octagonal symbol alphabets and algebraic number theory [PDF]
Journal of High Energy Physics, 2020 It is widely expected that NMHV amplitudes in planar, maximally supersymmetric Yang-Mills theory require symbol letters that are not rationally expressible in terms of momentum-twistor (or cluster) variables starting at two loops for eight particles. Re-
Jacob L. Bourjaily +5 more
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Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang, 2023 This study focused on students’ inability to correctly use psychometric tests applied for complex numbers in the context of generating an Algebraic abelian group (closure, commutative, associatively, inverse, and identity).
Idowu Oluwaseun Longe +1 more
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Multifractality of light in photonic arrays based on algebraic number theory [PDF]
Communications Physics, 2020 Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity that is mathematically described by fractal geometry.
Fabrizio Sgrignuoli +5 more
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Newton polygons of higher order in algebraic number theory [PDF]
, 2011 We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a p-adic eld, together with relevant arithmetic information about the elds generated by the irreducible factors.
Jordi Guàrdia +2 more
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Trace formalism for motivic cohomology [PDF]
Épijournal de Géométrie Algébrique, 2023 The goal of this paper is to construct trace maps for the six functor formalism of motivic cohomology after Voevodsky, Ayoub, and Cisinski-D\'{e}glise. We also construct an $\infty$-enhancement of such a trace formalism.
Tomoyuki Abe
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Density of Arithmetic Representations of Function Fields [PDF]
Épijournal de Géométrie Algébrique, 2022 We propose a conjecture on the density of arithmetic points in the deformation space of representations of the \'etale fundamental group in positive characteristic. This?
Hélène Esnault, Moritz Kerz
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Etale and crystalline companions, I [PDF]
Épijournal de Géométrie Algébrique, 2022 Let $X$ be a smooth scheme over a finite field of characteristic $p$. Consider the coefficient objects of locally constant rank on $X$ in $\ell$-adic Weil cohomology: these are lisse Weil sheaves in \'etale cohomology when $\ell \neq p$, and ...
Kiran S. Kedlaya
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Optimal Ate Pairing on Elliptic Curves with Embedding Degree $9,15$ and $27$ [PDF]
Groups, Complexity, Cryptology, 2020 Much attention has been given to the efficient computation of pairings on elliptic curves with even embedding degree since the advent of pairing-based cryptography.
Emmanuel Fouotsa +2 more
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Algebraic, Analytic, and Computational Number Theory and Its Applications
Mathematics, 2023 Analytic number theory is a branch of number theory which inherits methods from mathematical analysis in order to solve difficult problems about the integers [...]
Diana Savin +2 more
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