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arXiv · 2606.05504

The Sharp Sadov Constant and Local Spectral Stability for Shapiro--Diananda Cyclic Sums

Denis Sheremet
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Abstract

We determine the sharp Sadov constant for Shapiro--Diananda cyclic sums. Sadov proved the lower bound C >= log 2; we prove the matching upper bound by an explicit asymptotic construction, obtaining C = log 2. We also develop a local spectral stability theory for the equal point of the Shapiro--Diananda cyclic sums. The Hessian is diagonalized by Fourier modes, giving an exact local minimum/saddle/quadratic-degeneracy criterion for all n and k, periodic equality families, and explicit classifications for k = 2 and k = 3. The result determines the global infimum over all n and k, but does not solve the separate fixed-k asymptotic minimization problems.

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Denis Sheremet. 2026-06-03. The Sharp Sadov Constant and Local Spectral Stability for Shapiro--Diananda Cyclic Sums. https://doi.org/10.5281/zenodo.20533489

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