§27.1 Special Notation

Keywords:: additive number theory, multiplicative number theory, number theory, partition, primes
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	positive integers (unless otherwise indicated).
$d\divides n$	divides .
$\left(m,n\right)$	greatest common divisor of . If $\left(m,n\right)=1$ , and 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 .
$\sum_{{\left(m,n\right)=1}}$	sum taken over , $1\leq m\leq n$ and relatively prime to .
$p,p_{1},p_{2},\dots$	prime numbers (or primes): integers () with only two positive integer divisors, 1 and the number itself.
$\sum_{p}$ , $\prod_{p}$	sum, product extended over all primes.
	real numbers.
$\sum_{{n\leq x}}$	$\sum_{{n=1}}^{{\left\lfloor x\right\rfloor}}$ .
$\mathop{\mathrm{log}\,\/}\nolimits x$	natural logarithm of , 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.