## a-

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 19 words.

Prefix meaning ‘not’. For example, an asymmetric figure is one which possesses no symmetry, which is not symmetrical.

## A

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 7 words.

The number 10 in hexadecimal notation.

## A

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 7 words.

The number 10 in hexadecimal notation.

## a-

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 19 words.

Prefix meaning ‘not’. For example, an asymmetric figure is one which possesses no symmetry, which is not symmetrical.

##
*A + B = C* and big III's

in** The Quarterly Journal of Mathematics**

March 1998; p ublished online March 1998 .

Journal Article. Subjects: Pure Mathematics. 0 words.

Assuming standard conjectures we show that there exist elliptic curves with Tate-Shafarevich group of order essentially as large as the square root of the conductor. We present some...

Go to
** » ** abstract

## A “Bottom Up” Characterization of Smooth Deligne–Mumford Stacks

in** International Mathematics Research Notices**

November 2017; p ublished online September 2016 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 5814 words.

**Abstract**

We prove a structure theorem for relative coarse space morphisms from smooth Deligne–Mumford stacks, showing that each such map can be decomposed in...

## A [math] lower bound for the border rank of matrix multiplication

in** International Mathematics Research Notices**

August 2018; p ublished online March 2017 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 4980 words.

**Abstract**

Let [math] denote the matrix multiplication tensor for [math] matrices. We use the border substitution method [2, 3, 6] combined with Koszul...

## abacus

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 26 words.

A counting device consisting of rods on which beads can be moved so as to represent numbers.

## abacus

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 26 words.

A counting device consisting of rods on which beads can be moved so as to represent numbers.

##
The *abc* theorem for commutative algebraic groups in characteristic *p*

in** International Mathematics Research Notices**

January 1997; p ublished online January 1997 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

## Abel, Niels Henrik (1802–29)

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 94 words.

who, at the age of 19, proved that the general equation of degree greater than 4 cannot be solved algebraically.

## Abel, Niels Henrik (1802–29)

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 94 words.

who, at the age of 19, proved that the general equation of degree greater than 4 cannot be solved algebraically. In other words, there can be no formula for the roots of such an equation...

## Abel summation

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 40 words.

A method of computing the sum of a possibly *divergent series of *complex numbers as the limit, as ...

## Abel’s Limit Theorem

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 30 words.

For a *convergent series {*a _{k}
*}, the limit assigned by the Abel summation method exists and is equal to the sum of the series....

## Abel’s partial summation formula

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 25 words.

For two arbitrary sequences and with , the result that . This has some similarities with the formula for *integration by parts....

## Abel’s test

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 49 words.

A test for the convergence of an infinite series which states that if ∑*a*
_{
n
} is a convergent sequence, and {...

## Abelian 1-Calabi–Yau Categories

in** International Mathematics Research Notices**

January 2008; p ublished online January 2008 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

In this paper, we show all *k*-linear abelian 1-Calabi–Yau categories over an algebraically closed field *k* are derived equivalent to either the category of coherent sheaves on an elliptic...

## Abelian Functions for Trigonal Curves of Genus Three

in** International Mathematics Research Notices**

January 2007; p ublished online January 2007 .

Journal Article. Subjects: Mathematics; Pure Mathematics. 0 words.

We develop the theory of generalized Weierstrass σ- and ℘-functions defined on a general trigonal curve of genus three. In particular, we give a list of the associated partial differential...

## abelian group

in** The Concise Oxford Dictionary of Mathematics**

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 38 words.

Suppose that *G* is a *group with the operation ￮. Then *G* is abelian if the operation ￮ is

## abelian group

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 41 words.

Suppose that *G* is a *group with the operation ￮. Then *G* is abelian if the operation ￮ is commutative; that is, if, for all elements ...