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27 Functions of Number Theory Notation 27 Functions of Number Theory 27.2 Functions

§27.1 Special Notation

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Defines:: $\left(\NVar{m},\NVar{n}\right)$ : greatest common divisor (gcd)
Keywords:: additive number theory, multiplicative number theory, notation, number theory, partition, primes
Permalink:: http://dlmf.nist.gov/27.1
See also:: Annotations for Ch.27

(For other notation see Notation for the Special Functions.)

$d, k, m, n$	positive integers (unless otherwise indicated).
$d\mathbin{\|}n$	$d$ divides $n$ .
$\left(m,n\right)$	greatest common divisor of $m, n$ . If $\left(m,n\right)=1$ , $m$ and $n$ are called relatively prime, or coprime.
$\left(d_{1},\dots,d_{n}\right)$	greatest common divisor of $d_{1},\dots,d_{n}$ .
$\sum_{d\mathbin{\|}n}$ , $\prod_{d\mathbin{\|}n}$	sum, product taken over divisors of $n$ .
$\sum_{\left(m,n\right)=1}$	sum taken over $m$ , $1\leq m\leq n$ and $m$ relatively prime to $n$ .
$p,p_{1},p_{2},\dots$	prime numbers (or primes): integers ( $>1$ ) with only two positive integer divisors, $1$ and the number itself.
$\sum_{p}$ , $\prod_{p}$	sum, product extended over all primes.
$x, y$	real numbers.
$\sum_{n\leq x}$	$\sum_{n=1}^{\left\lfloor x\right\rfloor}$ .
$\zeta\left(s\right)$	Riemann zeta function; see §25.2(i).
$(n\|P)$	Jacobi symbol; see §27.9.
$(n\|p)$	Legendre symbol; see §27.9.

27 Functions of Number Theory 27.2 Functions

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