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Introductory remarks on complex multiplication [PDF]
International Journal of Mathematics and Mathematical Sciences, 1982 Complex multiplication in its simplest form is a geometric tiling property. In its advanced form it is a unifying motivation of classical mathematics from elliptic integrals to number theory; and it is still of active interest.
Harvey Cohn
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Class fields generated by coordinates of elliptic curves
Open Mathematics, 2022 Let KK be an imaginary quadratic field different from Q(−1){\mathbb{Q}}\left(\sqrt{-1}) and Q(−3){\mathbb{Q}}\left(\sqrt{-3}). For a nontrivial integral ideal m{\mathfrak{m}} of KK, let Km{K}_{{\mathfrak{m}}} be the ray class field modulo m{\mathfrak{m}}.
Jung Ho Yun, Koo Ja Kyung, Shin Dong Hwa
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Accurate Complex Multiplication in Floating-Point Arithmetic [PDF]
, 2019 International audienceWe deal with accurate complex multiplication in binary floating-point arithmetic, with an emphasis on the case where one of the operands in a "double-word" number. We provide an algorithm that returns a complex product with normwise
Muller, Jean-Michel, Lefèvre, Vincent
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Level crossings, attractor points and complex multiplication
Journal of High Energy Physics, 2023 We study the complex structure moduli dependence of the scalar Laplacian eigenmodes for one-parameter families of Calabi-Yau n-folds in ℙ n+1. It was previously observed that some eigenmodes get lighter while others get heavier as a function of these ...
Hamza Ahmed, Fabian Ruehle
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Applied Sciences, 2023 Intelligence development has put forward increasing requirements of real-time planning and dynamic feedback in controlling robotic arms. It has become essential in engineering applications to complete the kinematics calculation of complex manipulators in
Jiyang Yu +4 more
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The Cayley-Dickson Construction in ACL2 [PDF]
Electronic Proceedings in Theoretical Computer Science, 2017 The Cayley-Dickson Construction is a generalization of the familiar construction of the complex numbers from pairs of real numbers. The complex numbers can be viewed as two-dimensional vectors equipped with a multiplication. The construction can be used
John Cowles, Ruben Gamboa
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Positive impact of sleep on recall of multiplication facts
Royal Society Open Science, 2023 This study tested the hypothesis that learning complex multiplication problems (e.g. 8 × 23 = 184) prior to sleep would benefit recall in adult participants compared with learning the problems prior to a period of wakefulness.
Jayne Spiller, Camilla Gilmore
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Slip-free multiplication and complexity of dislocation networks in FCC metals
Materials Theory, 2021 During plastic deformation of crystalline solids, intricate networks of dislocation lines form and evolve. To capture dislocation density evolution, prominent theories of crystal plasticity assume that 1) multiplication is driven by slip in active slip ...
Sh. Akhondzadeh +3 more
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On some extensions of Gauss’ work and applications
Open Mathematics, 2020 Let K be an imaginary quadratic field of discriminant dK{d}_{K} with ring of integers OK{{\mathcal{O}}}_{K}, and let τK{\tau }_{K} be an element of the complex upper half plane so that OK=[τK,1]{{\mathcal{O}}}_{K}={[}{\tau }_{K},1].
Jung Ho Yun, Koo Ja Kyung, Shin Dong Hwa
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Multiplications on a Complex [PDF]
The Annals of Mathematics, 1936 In their communications at the First International Topological Conference (Moscow, September 1935), J. W. Alexander and A. Kolmogoroff introduced the notion of a dual cycle1 and defined a product of a dual p-eycle and a dual q-eycle, this product being a dual (p + q)-eyele. A different multiplication of the same sort is considered in this paper. It may
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