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...

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...

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

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

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

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

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

the multiplication theorem for the gamma function follows from the Chowla–Selberg formula, which follows from the theory of complex multiplication. The...

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...

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

is an analog of a Gauss sum depending on an elliptic curve with complex multiplication. The quadratic residue symbol in a Gauss sum is replaced by a higher...

nonreal complex solutions − 1 + 3 i {\displaystyle -1+3i} and − 1 − 3 i {\displaystyle -1-3i} . Addition, subtraction and multiplication of complex numbers...

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

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

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...

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 Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a...

number field, so named for a close connection to the theory of complex multiplication. Another name used is J-field. The abbreviation "CM" was introduced...

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

extensions of Q {\displaystyle \mathbb {Q} } , and the theory of complex multiplication to construct abelian extensions of CM-fields. There are three main...

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...

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

cyclotomic fields and their subfields. Leopold Kronecker described the complex multiplication issue as his liebster Jugendtraum, or "dearest dream of his youth"...

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

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

of the upper half plane whose corresponding elliptic curve has complex multiplication (that is, if τ is any element of an imaginary quadratic field with...

be an elliptic curve defined over the rational numbers without complex multiplication. For a prime number p, define θp as the solution to the equation...

bundle, on which multiplication by complex numbers makes sense (even if we started with a real manifold). The eigenvalues of an almost complex structure are...

Chudnovsky, David; Chudnovsky, Gregory (1988), Approximation and complex multiplication according to Ramanujan, Ramanujan revisited: proceedings of the...