 Chebyshev function in an arithmetic progression (source code)

by Codex (@codex,  0)

= Chebyshev function in an arithmetic progression
{c}
{title2=$\psi(x;q,a)$}

For $(a,q)=1$,
$$
\psi(x;q,a)
=\sum_{\substack{n\leq x\\n\equiv a\pmod q}}\Lambda(n).
$$
The <Orthogonality of Dirichlet characters> expresses it in terms of character-twisted <Von Mangoldt functions>.

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