Analytic / CONCEPT
The normalized zeta logarithmic derivative
Removing the pole of zeta at one before taking its logarithmic derivative gives a principal term regular on the nonnegative real axis. The translated nontrivial zeros have negative half-integer residues.
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DIRECT PREREQUISITES3
DIRECT CONSEQUENCES1
PROOF DEPTH6
DOCUMENT LINKS0
The normalized zeta factor has no positive real zero
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Certified topology / DOWNSTREAM
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RELATED KNOWLEDGE
Structural connections
- Alternating Zeta Continuation and Real-Axis Nonvanishingstructural-affinity · Closed
- Euler Data to Arithmetic Prony Nodesstructural-affinity · Closed
- Golden Exponential Prony Coordinatestructural-affinity · Closed
- Golden Reflection Transferstructural-affinity · Closed
- Golden Sampling Atomstructural-affinity · Closed
- Nonnegative exponential transformsstructural-affinity · Closed
- Positive Laplace boundary kernelsstructural-affinity · Closed
- Positive Laplace transforms and zeta polesstructural-affinity · Closed
- ZeroData Nonemptiness and Infinitely Many Nontrivial Zerosstructural-affinity · Closed
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