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Aug 3 at 14:00 comment added Peter Humphries For congruence subgroups of $\mathrm{SL}_2(\mathbb{Z})$, this Dirichlet series is essentially a ratio of zeta functions or $L$-functions, and in this case $b_j = 1$. But perhaps these subgroups are not "typical".
Aug 3 at 11:04 history edited YCor CC BY-SA 4.0
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Aug 3 at 10:31 history asked Alexander Kalmynin CC BY-SA 4.0