Geodesic
Representation of Certain Logarithmic Functions as Polynomials with a Small Number of Nonzero Coefficients
Matematičeskie zametki, Tome 92 (2012) no. 1, pp. 68-73.

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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
Mots-clés : $p$-adic logarithm. 
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     title = {Representation of {Certain} {Logarithmic} {Functions} as {Polynomials} with a {Small} {Number} of {Nonzero} {Coefficients}},
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V. S. Rainchik. Representation of Certain Logarithmic Functions as Polynomials with a Small Number of Nonzero Coefficients. Matematičeskie zametki, Tome 92 (2012) no. 1, pp. 68-73. http://geodesic.mathdoc.fr/item/MZM_2012_92_1_a6/

[1] V. V. Nazarov, Ob ispolzovanii svoistva kommutirovaniya simvola stepennogo vycheta v skhemakh otkrytogo raspredeleniya klyucha, Dis. $\dots$ kand. fiz.-matem. nauk, MGU, M., 2006

[2] E. Artin, J. Tate, Class Field Theory, W. A. Benjamin, New York, 1968 | MR | Zbl

[3] M. A. Cherepnev, “Skhemy otkrytogo raspredeleniya klyuchei na osnove nekommutativnoi gruppy”, Diskret. matem., 15:2 (2003), 47–51 | MR | Zbl