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Journal articles on the topic 'Multiplication, Complex'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Kibelbek, Jonas, Ling Long, Kevin Moss, Benjamin Sheller, and Hao Yuan. "Supercongruences and complex multiplication." Journal of Number Theory 164 (July 2016): 166–78. http://dx.doi.org/10.1016/j.jnt.2015.12.013.

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2

Carocca, Angel, Herbert Lange, and Rubí E. Rodríguez. "Jacobians with complex multiplication." Transactions of the American Mathematical Society 363, no. 12 (2011): 6159–75. http://dx.doi.org/10.1090/s0002-9947-2011-05560-1.

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3

Fam, A. T. "Efficient complex matrix multiplication." IEEE Transactions on Computers 37, no. 7 (1988): 877–79. http://dx.doi.org/10.1109/12.2236.

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4

Eum, Ick Sun, Ho Yun Jung, Ja Kyung Koo, and Dong Hwa Shin. "Composition law and complex multiplication." Journal of Number Theory 209 (April 2020): 396–420. http://dx.doi.org/10.1016/j.jnt.2019.09.005.

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5

Polishchuk, A. "Theta identities with complex multiplication." Duke Mathematical Journal 96, no. 2 (1999): 377–400. http://dx.doi.org/10.1215/s0012-7094-99-09611-4.

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6

Zarhin, Yuri G. "Hyperelliptic jacobians without complex multiplication." Mathematical Research Letters 7, no. 1 (2000): 123–32. http://dx.doi.org/10.4310/mrl.2000.v7.n1.a11.

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7

Connes, Alain, Matilde Marcolli, and Niranjan Ramachandran. "KMS states and complex multiplication." Selecta Mathematica 11, no. 3-4 (2005): 325–47. http://dx.doi.org/10.1007/s00029-005-0013-x.

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8

Grabauskienė, Vaiva, and Oksana Mockaitytė-Rastenienė. "AN EXPRESSION OF MATHEMATICAL CONNECTIONS IN MULTIPLICATION-RELATED THINKING IN THIRD AND FOURTH GRADES OF PRIMARY SCHOOL." ŠVIETIMAS: POLITIKA, VADYBA, KOKYBĖ / EDUCATION POLICY, MANAGEMENT AND QUALITY 11, no. 1 (2019): 9–29. http://dx.doi.org/10.48127/spvk-epmq/19.11.09.

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Mathematical comprehension is closely related to a cognition of mathematical connections. A multiplication is a mathematical operation characterized by complex mathematical connections. Students are early introduced with the multiplication. Therefore, in primary school, not so developed cognition of mathematical connections may become a reason for difficulties in Maths. A functionality of concept is based on a view to a multiplication. The analysis scientific literature revealed that a thinking of multiplication can be either additive or multiplicative. Additionally, the multiplication learnin

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9

Chang, Sungkon. "Complex multiplication of two eta-products." Colloquium Mathematicum 159, no. 1 (2020): 7–24. http://dx.doi.org/10.4064/cm7134-12-2018.

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10

Morton, Patrick. "Legendre polynomials and complex multiplication, I." Journal of Number Theory 130, no. 8 (2010): 1718–31. http://dx.doi.org/10.1016/j.jnt.2010.03.009.

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11

Goren, Eyal Z., and Kristin E. Lauter. "Genus 2 Curves with Complex Multiplication." International Mathematics Research Notices 2012, no. 5 (2011): 1068–142. http://dx.doi.org/10.1093/imrn/rnr052.

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12

Rohde, Jan Christian. "Some mirror partners with complex multiplication." Communications in Number Theory and Physics 4, no. 3 (2010): 597–607. http://dx.doi.org/10.4310/cntp.2010.v4.n3.a3.

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13

Lenstra, Jr., H. W. "Complex Multiplication Structure of Elliptic Curves." Journal of Number Theory 56, no. 2 (1996): 227–41. http://dx.doi.org/10.1006/jnth.1996.0015.

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14

Sebbar, Abdellah. "Twisted L-Functions and Complex Multiplication." Journal of Number Theory 88, no. 1 (2001): 104–13. http://dx.doi.org/10.1006/jnth.2000.2613.

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15

Shuster, John A., and Jens Köplinger. "Elliptic complex numbers with dual multiplication." Applied Mathematics and Computation 216, no. 12 (2010): 3497–514. http://dx.doi.org/10.1016/j.amc.2010.04.069.

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16

Kersten, Ina, and Johannes Michaliček. "Zp-Extensions of complex multiplication fields." Journal of Number Theory 32, no. 2 (1989): 131–50. http://dx.doi.org/10.1016/0022-314x(89)90023-1.

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17

Ziobro, Rafał. "Multiplication-Related Classes of Complex Numbers." Formalized Mathematics 28, no. 2 (2020): 197–210. http://dx.doi.org/10.2478/forma-2020-0017.

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Summary The use of registrations is useful in shortening Mizar proofs [1], [2], both in terms of formalization time and article space. The proposed system of classes for complex numbers aims to facilitate proofs involving basic arithmetical operations and order checking. It seems likely that the use of self-explanatory adjectives could also improve legibility of these proofs, which would be an important achievement [3]. Additionally, some potentially useful definitions, following those defined for real numbers, are introduced.

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18

Howard, Benjamin. "Complex multiplication cycles and Kudla-Rapoport divisors." Annals of Mathematics 176, no. 2 (2012): 1097–171. http://dx.doi.org/10.4007/annals.2012.176.2.9.

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19

AIKAWA, Yusuke, Koji NUIDA, and Masaaki SHIRASE. "Elliptic Curve Method Using Complex Multiplication Method." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E102.A, no. 1 (2019): 74–80. http://dx.doi.org/10.1587/transfun.e102.a.74.

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20

Arnold, Trevor. "Complex multiplication and parity in Iwasawa theory." Journal of Number Theory 128, no. 9 (2008): 2634–54. http://dx.doi.org/10.1016/j.jnt.2008.02.005.

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21

Lynker, Monika, Vipul Periwal, and Rolf Schimmrigk. "Complex multiplication symmetry of black hole attractors." Nuclear Physics B 667, no. 3 (2003): 484–504. http://dx.doi.org/10.1016/s0550-3213(03)00454-1.

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22

Sadykov, Marat, Yasuo Asami, Hironori Niki, et al. "Multiplication of a restriction-modification gene complex." Molecular Microbiology 48, no. 2 (2003): 417–27. http://dx.doi.org/10.1046/j.1365-2958.2003.03464.x.

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23

Schoen, Chad. "Complex multiplication cycles on elliptic modular threefolds." Duke Mathematical Journal 53, no. 3 (1986): 771–94. http://dx.doi.org/10.1215/s0012-7094-86-05343-3.

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24

Liu, J., B. Weaver, and Y. Zakharov. "FPGA implementation of multiplication-free complex division." Electronics Letters 44, no. 2 (2008): 95. http://dx.doi.org/10.1049/el:20082567.

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25

Clark, Pete L., Patrick Corn, Alex Rice, and James Stankewicz. "Computation on elliptic curves with complex multiplication." LMS Journal of Computation and Mathematics 17, no. 1 (2014): 509–35. http://dx.doi.org/10.1112/s1461157014000072.

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AbstractWe give the complete list of possible torsion subgroups of elliptic curves with complex multiplication over number fields of degree 1–13. Additionally we describe the algorithm used to compute these torsion subgroups and its implementation.

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26

Brent, Richard, Colin Percival, and Paul Zimmermann. "Error bounds on complex floating-point multiplication." Mathematics of Computation 76, no. 259 (2007): 1469–82. http://dx.doi.org/10.1090/s0025-5718-07-01931-x.

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27

Stouraitis, Thanos, and Alexander Skavantzos. "Multiplication of complex numbers encoded as polynomials." Journal of VLSI signal processing systems for signal, image and video technology 3, no. 4 (1991): 319–28. http://dx.doi.org/10.1007/bf00936904.

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28

Parish, James L. "Rational torsion in complex-multiplication elliptic curves." Journal of Number Theory 33, no. 2 (1989): 257–65. http://dx.doi.org/10.1016/0022-314x(89)90012-7.

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29

Gukov, Sergei, and Cumrun Vafa. "Rational Conformal Field Theories and Complex Multiplication." Communications in Mathematical Physics 246, no. 1 (2004): 181–210. http://dx.doi.org/10.1007/s00220-003-1032-0.

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30

Katz, Curren, and André Knops. "Decreased cerebellar-cerebral connectivity contributes to complex task performance." Journal of Neurophysiology 116, no. 3 (2016): 1434–48. http://dx.doi.org/10.1152/jn.00684.2015.

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The cerebellum's role in nonmotor processes is now well accepted, but cerebellar interaction with cerebral targets is not well understood. Complex cognitive tasks activate cerebellar, parietal, and frontal regions, but the effective connectivity between these regions has never been tested. To this end, we used psycho-physiological interactions (PPI) analysis to test connectivity changes of cerebellar and parietal seed regions in complex (2-digit by 1-digit multiplication, e.g., 12 × 3) vs. simple (1-digit by 1-digit multiplication, e.g., 4 × 3) task conditions (“complex − simple”). For cerebel

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31

Kazal, Nurul Yakim, Imam Mukhlash, Bandung Arry Sanjoyo, Nurul Hidayat, and Katsuhisa Ozaki. "Extended use of error-free transformation for real matrix multiplication to complex matrix multiplication." Journal of Physics: Conference Series 1821, no. 1 (2021): 012022. http://dx.doi.org/10.1088/1742-6596/1821/1/012022.

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32

Fomin, Vasiliy I. "About unbounded complex operators." Russian Universities Reports. Mathematics, no. 129 (2020): 57–67. http://dx.doi.org/10.20310/2686-9667-2020-25-129-57-67.

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The concept of an unbounded complex operator as an operator acting in the pull-back of a Banach space is introduced. It is proved that each such operator is linear. Linear operations of addition and multiplication by a number and also the operation of multiplication are determined on the set of unbounded complex operators. The conditions for commutability of operators from this set are indicated. The product of complex conjugate operators and the properties of the conjugation operation are considered. Invertibility questions are studied: two contractions of an unbounded complex operator that h

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33

NAKAMURA, Tetsuo. "A classification of $Q$ -curves with complex multiplication." Journal of the Mathematical Society of Japan 56, no. 2 (2004): 635–48. http://dx.doi.org/10.2969/jmsj/1191418649.

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34

Andreatta, Fabrizio, Eyal Goren, Benjamin Howard, and Keerthi Madapusi Pera. "Faltings heights of abelian varieties with complex multiplication." Annals of Mathematics 187, no. 2 (2018): 391–531. http://dx.doi.org/10.4007/annals.2018.187.2.3.

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35

Schertz, Reinhard. "Global construction of associated orders in complex multiplication." Journal of Number Theory 111, no. 2 (2005): 197–226. http://dx.doi.org/10.1016/j.jnt.2004.10.010.

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36

Streng, Marco. "Divisibility sequences for elliptic curves with complex multiplication." Algebra & Number Theory 2, no. 2 (2008): 183–208. http://dx.doi.org/10.2140/ant.2008.2.183.

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37

James, Kevin, and Paul Pollack. "Extremal primes for elliptic curves with complex multiplication." Journal of Number Theory 172 (March 2017): 383–91. http://dx.doi.org/10.1016/j.jnt.2016.09.033.

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38

Howard, Benjamin. "Complex multiplication cycles and Kudla-Rapoport divisors, II." American Journal of Mathematics 137, no. 3 (2015): 639–98. http://dx.doi.org/10.1353/ajm.2015.0021.

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39

Coates, John. "Elliptic Curves with Complex Multiplication and Iswasawa Theory." Bulletin of the London Mathematical Society 23, no. 4 (1991): 321–50. http://dx.doi.org/10.1112/blms/23.4.321.

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40

Venter, Lucas. "A MULTIPLICATION INEQUALITY IN COMPLEX BANACH LATTICE ALGEBRAS." Quaestiones Mathematicae 8, no. 3 (1985): 275–81. http://dx.doi.org/10.1080/16073606.1985.9631916.

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41

Lynker, Monika, Rolf Schimmrigk, and Steven Stewart. "Complex multiplication of exactly solvable Calabi–Yau varieties." Nuclear Physics B 700, no. 1-3 (2004): 463–89. http://dx.doi.org/10.1016/j.nuclphysb.2004.08.007.

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42

Connolly, F. T., and A. E. Yagle. "Fast algorithms for complex matrix multiplication using surrogates." IEEE Transactions on Acoustics, Speech, and Signal Processing 37, no. 6 (1989): 938–39. http://dx.doi.org/10.1109/assp.1989.28064.

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43

Zarhin, Yuri G. "Hyperelliptic jacobians without complex multiplication in positive characteristic." Mathematical Research Letters 8, no. 4 (2001): 429–35. http://dx.doi.org/10.4310/mrl.2001.v8.n4.a3.

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44

NIKOLAEV, Igor V. "On a symmetry of complex and real multiplication." Hokkaido Mathematical Journal 45, no. 1 (2016): 43–51. http://dx.doi.org/10.14492/hokmj/1470080747.

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45

Kılıçer, Pınar, Hugo Labrande, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling, and Marco Streng. "Plane quartics over $\mathbb {Q}$ with complex multiplication." Acta Arithmetica 185, no. 2 (2018): 127–56. http://dx.doi.org/10.4064/aa170227-16-3.

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46

Zając, Sylwester. "The Hadamard multiplication theorem in several complex variables." Complex Variables and Elliptic Equations 62, no. 1 (2016): 1–26. http://dx.doi.org/10.1080/17476933.2016.1197918.

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47

Saikia, A. "Selmer Groups of Elliptic Curves with Complex Multiplication." Canadian Journal of Mathematics 56, no. 1 (2004): 194–208. http://dx.doi.org/10.4153/cjm-2004-009-7.

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AbstractSuppose K is an imaginary quadratic field and E is an elliptic curve over a number field F with complex multiplication by the ring of integers in K. Let p be a rational prime that splits as in K. Let Epn denote the pn-division points on E. Assume that F(Epn) is abelian over K for all n ≥ 0. This paper proves that the Pontrjagin dual of the -Selmer group of E over F(Ep∞) is a finitely generated free Λ-module, where Λ is the Iwasawa algebra of . It also gives a simple formula for the rank of the Pontrjagin dual as a Λ-module.

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48

Kumar Murty, V., and Vijay M. Patankar. "Tate Cycles on Abelian Varieties with Complex Multiplication." Canadian Journal of Mathematics 67, no. 1 (2015): 198–213. http://dx.doi.org/10.4153/cjm-2014-001-2.

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AbstractWe consider Tate cycles on an Abelian variety A defined over a sufficiently large number field K and having complexmultiplication. We show that there is an effective bound C = C(A, K) so that to check whether a given cohomology class is a Tate class on A, it suffices to check the action of Frobenius elements at primes v of norm ≤ C. We also show that for a set of primes v of K of density 1, the space of Tate cycles on the special fibre Av of the Néron model of A is isomorphic to the space of Tate cycles on A itself.

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49

Pontarelli, Salvatore, Pedro Reviriego, Chris J. Bleakley, and Juan Antonio Maestro. "Low Complexity Concurrent Error Detection for Complex Multiplication." IEEE Transactions on Computers 62, no. 9 (2013): 1899–903. http://dx.doi.org/10.1109/tc.2012.246.

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50

David, C., A. Gafni, A. Malik, N. Prabhu, and C. L. Turnage-Butterbaugh. "Extremal primes for elliptic curves without complex multiplication." Proceedings of the American Mathematical Society 148, no. 3 (2019): 929–43. http://dx.doi.org/10.1090/proc/14748.

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