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math.NT2026
Proof of Sun's conjectures on hyperbolic cosine series via the Eisenstein--Lambert method
Nikita Kalinin
We prove two conjectures of Zhi-Wei Sun concerning hyperbolic cosine Lambert series. The first one is the evaluation, for integers , of \[ S_m=\sum_{n=1}^\infty\left( \fra…
math.NT2026
Residues of a tropical zeta function for convex domains
Nikita Kalinin, Ernesto Lupercio, Mikhail Shkolnikov
We define an -invariant tropical zeta function of a convex domain. In dimension 2 it admits boundary Dirichlet-series representation with summands…
math.NT2025
Wolstenholme's theorem over Gaussian integers
Nikita Kalinin
This paper establishes an extension of Wolstenholme's theorem to the ring of Gaussian integers . For a prime , we prove that the sum of inverses of Gaus…