The numerical factors of Δ n (f, g)

Qingzhong Ji () and Hourong Qin ()
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Qingzhong Ji: Nanjing University
Hourong Qin: Nanjing University

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 5, 701-714

Abstract: Abstract Let α 1, α 2, ..., α r be the roots of the polynomial f(x) = x r + a 1 x r − 1 + ⋯ + a r ∈ ℤ[x] and let $$g = \{ g_n (X)\} _{n \in \mathbb{N}}$$ , where g n (X) = g n (x 1, x 2, ..., x r ∈ ℤ[x 1, x 2, ..., x r ] is a symmetric polynomial. For each n, put Δ n (f, g) = g n (α 1, α 2, ..., α r ). In this paper, for a special symmetric polynomial sequence g, we investigate the numerical factors of Δ n (f, g). If p is a prime, we establish an analogue of Iwasawa’s theorem in algebraic number theory for the orders $$ord_p \left( {\Delta _{np^t } \left( {f,g} \right)} \right)$$ of the p-primary part of $$\Delta _{np^t } \left( {f,g} \right)$$ when t varies.

Keywords: Recurring series; Iwasawa theory; cyclotomic polynomial (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s13226-015-0140-9

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