In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers. Put another way...

of vector multiplication or changing the sign of complex numbers. In arithmetic, multiplication is often written using the multiplication sign (either...

multiplication is commutative, associative and distributes over addition. Just as for complex numbers, one can define the notion of a split-complex conjugate...

A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient...

SL2(L) an additional structure can be imposed of a building with complex multiplication. These were first introduced by Martin L. Brown (Brown 2004). These...

an elliptic curve E D / C {\textstyle E_{D}/\mathbb {C} } with complex multiplication by Z [ τ D ] {\textstyle \mathbb {Z} [\tau _{D}]} , we have − 2...

+i\sin \theta .} (See Euler's formula.) Under the complex multiplication operation, the unit complex numbers form a group called the circle group, usually...

nonzero complex number has a multiplicative inverse. This makes the complex numbers a field with the real numbers as a subfield. The complex numbers also...

arithmetic geometry. He was known for developing the theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the...

subring in its endomorphism ring End(A). The terminology here is from complex multiplication theory, which was developed for elliptic curves in the nineteenth...

conjecture was first proved by Deuring (1941) for elliptic curves with complex multiplication. It was subsequently shown to be true for all elliptic curves over...

some sense with loss of explicit information (as is typical of several complex variables). The Manin–Mumford conjecture of Yuri Manin and David Mumford...

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on...

construct a curve E where the number of points is easy to compute. Complex multiplication is key in the construction of the curve. Now, given an N for which...

linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns...

define multiplication by complex scalars in a canonical fashion so as to regard V {\displaystyle V} as a complex vector space. Every complex vector space...

The complex plane allows for a geometric interpretation of complex numbers. Under addition, they add like vectors. The multiplication of two complex numbers...

hence their coefficients, like quaternions. Multiplication of octonions is more complex. Multiplication is distributive over addition, so the product...

Benedict Gross's Harvard University homepage "Benedict Gross "Complex Multiplication: Past, Present, Future" Lecture 1". YouTube. January 30, 2019. Archived...

the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers...

The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a divide-and-conquer...

complex structure J {\displaystyle J} (different multiplication by i {\displaystyle i} ). If V {\displaystyle V} and W {\displaystyle W} are complex vector...

mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity...

consisting of a set together with operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms...

numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i. Imaginary...

in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication. When matrices or...

BBC. 「遺書」、『谷山豊全集』新版 p.324 Shimura, Goro; Taniyama, Yutaka (1961), Complex multiplication of abelian varieties and its applications to number theory, Publications...

In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract...

complex multiplications (again, ignoring simplifications of multiplications by 1 and similar) and n log 2 ⁡ ( n ) {\textstyle n\log _{2}(n)} complex additions...

quaternion addition and multiplication correspond to matrix addition and matrix multiplication. One is to use 2 × 2 complex matrices, and the other is...