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theorem proved term proof

norm_eulerPrimeLogDerivTermComplex_le_carrierDerivTerm

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formal statement (Lean)

 522theorem norm_eulerPrimeLogDerivTermComplex_le_carrierDerivTerm {s : ℂ} (hs : 0 < s.re)
 523    (p : Nat.Primes) :
 524    ‖eulerPrimeLogDerivTermComplex p s‖ ≤ carrierDerivTerm p s.re := by

proof body

Term-mode proof.

 525  calc ‖eulerPrimeLogDerivTermComplex p s‖
 526      ≤ primeLog p * ‖eulerPrimePowerComplex p s‖ ^ 2 /
 527          (1 - ‖eulerPrimePowerComplex p s‖) :=
 528        norm_eulerPrimeLogDerivTermComplex_le hs p
 529    _ = carrierDerivTerm p s.re :=
 530        norm_form_eq_carrierDerivTerm p s
 531
 532/-- The complex Euler log-derivative terms are summable on `Re(s) > 1/2`.
 533Lifts `carrierDerivBound_summable` to the complex setting via the
 534per-prime domination bound. -/

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