Theorems · Theorem · number theory
ZMod.LFunction_residue_one
∀ {N : ℕ} [inst : NeZero N] (Φ : ZMod N → ℂ),
Filter.Tendsto (fun s => (s - 1) * ZMod.LFunction Φ s) (nhdsWithin 1 {1}ᶜ) (nhds (∑ j, Φ j / ↑N))The L-function of Φ has a residue at s = 1 equal to the average value of Φ.
- Defined in
- Mathlib.NumberTheory.LSeries.ZMod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NeZero
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Cites26
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- nhdsWithinstatement and proof · cited by 1,912
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