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27 Functions of Number TheoryNotation

§27.1 Special Notation

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

d,k,m,n positive integers (unless otherwise indicated).
d|n d divides n.
(m,n) greatest common divisor of m,n. If (m,n)=1, m and n are called relatively prime, or coprime.
(d1,,dn) greatest common divisor of d1,,dn.
d|n, d|n sum, product taken over divisors of n.
(m,n)=1 sum taken over m, 1mn and m relatively prime to n.
p,p1,p2, prime numbers (or primes): integers (>1) with only two positive integer divisors, 1 and the number itself.
p, p sum, product extended over all primes.
x,y real numbers.
nx n=1x.
logx natural logarithm of x, written as lnx in other chapters.
ζ(s) Riemann zeta function; see §25.2(i).
(n|P) Jacobi symbol; see §27.9.
(n|p) Legendre symbol; see §27.9.