§27.1 Special Notation

Keywords:: additive number theory, multiplicative number theory, number theory, partition, primes
Permalink:: http://dlmf.nist.gov/27.1

$d,k,m,n$	positive integers (unless otherwise indicated).
$d\divides n$	$d$ 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 $d_{1},\dots,d_{n}$ .
$\sum _{{d\divides n}}$ , $\prod _{{d\divides n}}$	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.
$\sum _{{n\leq x}}$	$\sum _{{n=1}}^{{\left\lfloor x\right\rfloor}}$ .
$\mathop{\mathrm{log}\,\/}\nolimits x$	natural logarithm of $x$ , written as $\mathop{\ln\/}\nolimits x$ in other chapters.
$\mathop{\zeta\/}\nolimits\!\left(s\right)$	Riemann zeta function; see §25.2(i).
$\mathop{(n\|P)\/}\nolimits$	Jacobi symbol; see §27.9.
$\mathop{(n\|p)\/}\nolimits$	Legendre symbol; see §27.9.