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math.NT2026

Linear recurrences and rational Lambert series

Igor Rivin

For a sequence , define \[ L_γ(z):=\sum_{n\ge 1}γ_n\frac{z^n}{1-z^n} =\sum_{n\ge 1}\Bigl(\sum_{d\mid n}γ_d\Bigr)z^n. \] We prove a short rigidity theorem: if…

math.NT2026

Monte-Carlo Irreducibility and Imprimitivity Detection of Polynomials over

Igor Rivin

We study fast Monte-Carlo methods for testing irreducibility and detecting arithmetic imprimitivity of polynomials over . Building on the subset-sum criterion of Pemant…

math.NT2025

Counting Matrices in SL3(Z) with Fixed Completely Split Character Polynomial: Preliminary Upper Bounds

Igor Rivin

We count matrices in the special linear group SL(n, Z) whose characteristic polynomials split completely over Q.