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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2012, Volume 92, Issue 1, Pages 68–73 (Mi mz9037)

Representation of Certain Logarithmic Functions as Polynomials with a Small Number of Nonzero Coefficients

V. S. Rainchik

M. V. Lomonosov Moscow State University

Abstract: We study an element of the ring of algebraic integers having the special form $1-z\lambda$. We obtain a formula for calculating its logarithmic functions. Thus, we verify the conjecture that logarithmic functions of the element $1-z\lambda$ are polynomials in $z$ such that $z$ appears only in powers that are divisors of the number of the logarithmic function.

Keywords: logarithmic function, algebraic integer of the form $1-z\lambda$, ring of algebraic integers, algebraic extension of a field, $p$-adic logarithm

DOI: https://doi.org/10.4213/mzm9037

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English version:
Mathematical Notes, 2012, 92:1, 64–69

Bibliographic databases:

UDC: 511.2
Revised: 08.12.2011

Citation: V. S. Rainchik, “Representation of Certain Logarithmic Functions as Polynomials with a Small Number of Nonzero Coefficients”, Mat. Zametki, 92:1 (2012), 68–73; Math. Notes, 92:1 (2012), 64–69

Citation in format AMSBIB
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