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

$d,k,m,n$ | positive integers (unless otherwise indicated). |
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$d|n$ | $d$ 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. |

$\left({d}_{1},\mathrm{\dots},{d}_{n}\right)$ | greatest common divisor of ${d}_{1},\mathrm{\dots},{d}_{n}$. |

${\sum}_{d|n}$, ${\prod}_{d|n}$ | sum, product taken over divisors of $n$. |

${\sum}_{\left(m,n\right)=1}$ | sum taken over $m$, $1\le m\le n$ and $m$ relatively prime to $n$. |

$p,{p}_{1},{p}_{2},\mathrm{\dots}$ | 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. |

${\sum}_{n\le x}$ | ${\sum}_{n=1}^{\lfloor x\rfloor}$. |

$\mathrm{log}x$ | natural logarithm of $x$, written as $\mathrm{ln}x$ in other chapters. |

$\zeta \left(s\right)$ | Riemann zeta function; see §25.2(i). |

$\left(n\right|P)$ | Jacobi symbol; see §27.9. |

$\left(n\right|p)$ | Legendre symbol; see §27.9. |