##
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.

##
Abel summation

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 37 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. 26 words.

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

##
Abel’s partial summation formula

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 26 words.

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

##
Abel’s test

in** The Concise Oxford Dictionary of Mathematics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 46 words.

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

##
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. 38 words.

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

##
Abelian Varieties

in** Fourier-Mukai Transforms in Algebraic Geometry**

April 2006; p ublished online September 2007 .

Chapter. Subjects: Geometry. 19346 words.

Historically, Mukai's equivalence with the Poincare bundle on the product of an abelian variety and its dual as kernel was the fist Fourier-Mukai transform. The first section in this...