N. Kalinin

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20242026

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math.GM2026

Lucas recurrences and Lambert series in coprime double sums

Nikita Kalinin

For the Lucas numbers $L_{0} = 2$ , $L_{1} = 1$ , and $L_{n} = L_{n - 1} + L_{n - 2}$ , we obtain \[ \sum_{\substack{n,m\ge1\\(n,m)=1}}\frac{1}{L_{2n}L_{2m}L_{2(n+m)}}=\frac1{45}. \] This follows from…

math.GM2026

Continued fractions, determinant expressions, and identities

Nikita Kalinin, Takao Komatsu

In this paper, we clarified the relationship between continued fractions, determinants, and identities, making it easier to apply these methods systematically in other settings. In…

math.GM2026

Error terms for continued fractions of $e^{1/ s}$ and $\frac{v}{u} tanh (\frac{1}{uv})$

Nikita Kalinin, Takao Komatsu

Many classical identities arise from nothing more mysterious than looking at the same object in two different ways. A number, a function, or a combinatorial object may admit severa…

math.GM2024

Legendre duality for certain summations over the Farey pairs

Nikita Kalinin

Each irreducible fraction $p / q > 0$ corresponds to a primitive vector $(p, q) \in Z^{2}$ with positive coordinates. Such a vector $(p, q)$ can be uniquely written as the sum of two…

Lucas recurrences and Lambert series in coprime double sums

Continued fractions, determinant expressions, and identities

Error terms for continued fractions of e1/s and uv​​tanh(uv​1​)

Legendre duality for certain summations over the Farey pairs

Error terms for continued fractions of $e^{1/ s}$ and $\frac{v}{u} tanh (\frac{1}{uv})$