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Black Hole Attractor Varieties and Complex Multiplication [PDF]
, 2003 Black holes in string theory compactified on Calabi-Yau varieties a priori might be expected to have moduli dependent features. For example the entropy of the black hole might be expected to depend on the complex structure of the manifold.
M. Lynker +2 more
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Some Mirror partners with Complex multiplication [PDF]
, 2010 In this note we provide examples of families of Calabi-Yau 3-manifolds over Shimura varieties, whose mirror families contain subfamilies over Shimura varieties.
Jan Christian Rohde
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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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Complex Multiplication Tests for Elliptic Curves [PDF]
, 2004 We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized algorithm can
Denis Charles
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A Rigorous Extension of the Schönhage-Strassen Integer Multiplication Algorithm Using Complex Interval Arithmetic [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 Multiplication of n-digit integers by long multiplication requires O(n^2) operations and can be time-consuming. In 1970 A. Schoenhage and V. Strassen published an algorithm capable of performing the task with only O(n log(n)) arithmetic operations over ...
Thomas Steinke, Raazesh Sainudiin
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Complex multiplication, rationality and mirror symmetry for Abelian varieties [PDF]
, 2008 We show that complex multiplication on abelian varieties is equivalent to the existence of a constant rational K\"ahler metric. We give a sufficient condition for a mirror of an abelian variety of CM-type to be of CM-type as well.
Meng Chen
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Faster quantum subroutine for matrix chain multiplication via Chebyshev approximation [PDF]
Scientific ReportsMatrix operations are crucial to various computational tasks in various fields, and quantum computing offers a promising avenue to accelerate these operations. We present a quantum matrix multiplication (QMM) algorithm that employs amplitude encoding and
Xinying Li +5 more
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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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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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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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