N. Kalinin

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math.NT2026

Weighted error-sum identities for periodic continued fractions and their generalizations

Kevin Calderon, Nikita Kalinin

For a purely $N$ -periodic continued fraction $I^¾ = [a_{0}, a_{1}, \dots, a_{N - 1}] = [a_{0}, a_{1}, \dots]$ , with $a_{k} = a_{k + N}$ for all $k \geq 0$ , and convergents $h_n/k_n=[a_0,a_1,\dots,…

math.NT2025

Evaluation of lattice sums via telescoping over topographs

Nikita Kalinin

Topographs, introduced by Conway in 1997, are infinite trivalent planar trees used to visualize the values of binary quadratic forms. In this work, we study series whose terms are…