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math.NT 1

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2026 1

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A note on the $q$-adic valuation of $\sigma_k(n)$

math.NT · 2026-05-18 · unverdicted · novelty 4.0

Exact formula for v_q(σ_k(n)) derived via LTE lemma and cyclotomic polynomials, yielding improved upper bound over Zhao for large n and k ≥ q-2.

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  • A note on the $q$-adic valuation of $\sigma_k(n)$ math.NT · 2026-05-18 · unverdicted · none · ref 8

    Exact formula for v_q(σ_k(n)) derived via LTE lemma and cyclotomic polynomials, yielding improved upper bound over Zhao for large n and k ≥ q-2.