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Ellipse conjecture for the roots of the Fibonacci-level characteristic polynomial
Ellipse conjecture. The roots of $f_n(\lambda)=F_{n+1}$ lie on an ellipse.
Conjectureopenfibonacci-sequence polynomial-rootsarXiv posted 2 days ago
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The Fibonacci replacement conjecture for t-metric Mahler measures
Fix an integer $N\geq3$ , a pair of primes $(p,q)$ satisfying the paper's compatibility condition, and the associated algebraic numbers $\alpha_n$ , functions $f_{\mathbf x}(t)$ , and…
Conjectureopenfibonacci-sequence mahler-measure number-theoryarXiv posted 2 days ago

Ellipse conjecture for the roots of the Fibonacci-level characteristic polynomial