Theorems · Theorem · number theory
LSeries_deriv_eqOn
∀ {f : ℕ → ℂ}, Set.EqOn (deriv (LSeries f)) (-LSeries (LSeries.logMul f)) {s | LSeries.abscissaOfAbsConv f < ↑s.re}The derivative of the L-series of f agrees with the negative of the L-series of
log * f on the right half-plane of absolute convergence.
- Defined in
- Mathlib.NumberTheory.LSeries.Deriv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredstatement and proof · cited by 6,101
- Complexstatement and proof · cited by 5,565
- Complex.restatement and proof · cited by 882
- ERealstatement · cited by 793
- derivstatement · cited by 676
- Set.EqOnstatement · cited by 603
- Real.toERealstatement and proof · cited by 303
- HasDerivAt.hasDerivWithinAtproof · cited by 86
- LSeriesstatement · cited by 77
- LSeries.abscissaOfAbsConvstatement and proof · cited by 50
- LSeries.logMulstatement · cited by 11
- deriv_eqOnproof · cited by 7
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