# Divisors

### Some articles on divisors, divisor:

Elementary Divisors
... In algebra, the elementary divisors of a module over a principal ideal domain (PID) occur in one form of the structure theorem for finitely generated modules over a principal ideal domain ... up to associatedness, and are called the elementary divisors ... primary ideals are powers of primes, so the elementary divisors ...
Mathukumalli V. Subbarao
... He also researched special classes of divisors and the corresponding analogues of divisor functions and perfect numbers, such as those arising from the exponential divisors ("e-divisors ...
Jacobi's Four-square Theorem
1 The number of ways to represent n as the sum of four squares is eight times the sum of the divisors of n if n is odd and 24 times the sum of the odd divisors ...
Ramanujan's Sum - Ramanujan Expansions - σk(n)
... σk(n) is the divisor function (i.e ... the sum of the kth powers of the divisors of n, including 1 and n) ... σ0(n), the number of divisors of n, is usually written d(n) and σ1(n), the sum of the divisors of n, is usually written σ(n) ...
Brill–Noether Theory
... theory, introduced by Brill and Noether (1874), is the study of special divisors, certain divisors on a curve C that determine more compatible functions than would be predicted ... In classical language, special divisors move on the curve in a "larger than expected" linear system of divisors ... The condition to be a special divisor D can be formulated in sheaf cohomology terms, as the non-vanishing of the H1 cohomology of the sheaf of the sections of the invertible sheaf or line bundle associated to D ...