Fuchs’s conjecture
For every entire function of order with , the deficiency of as a value of its logarithmic derivative vanishes: .
References
Primary source
Additional references
- A counterexample to Fuchs's conjecture — arXiv — Alexandre Eremenko, Teng Zhang
Progress summary
A new preprint claims to disprove Fuchs’s conjecture by giving an example that violates its universal prediction, but the result has not yet been independently confirmed.
Fuchs’s conjecture asserts that the deficiency at zero of the relevant logarithmic derivative must vanish. The reported construction would disprove this universal statement.
September 2026 counterexample
Alexandre Eremenko and Teng Zhang report a counterexample in the unrefereed preprint A counterexample to Fuchs's conjecture. Its construction gives a deficient logarithmic derivative at zero, contradicting Fuchs’s assertion and therefore claiming to settle the problem negatively. The claim is unverified.
Current status (as of September 2026): A counterexample has been reported by Eremenko and Teng Zhang, but its correctness remains unverified.
Solutions 0
No solutions have been posted yet.