Commit 2025-02-09 19:16 00672d34
View on Github →feat(NumberTheory/LSeries): results involving partial sums of coefficients (part 2) (#20660)
We prove the following result : if f : ℕ → ℂ
is such that (∑ k ∈ Icc 1 n, f k) / n
tends to some complex number l
when n → ∞
and that the L-series LSeries f
converges for all s : ℝ
such that 1 < s
, then (s - 1) * LSeries f s
tends to l
when s → 1
with 1 < s
.