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Aspects of Number Theory in Terms of Potential Theory

Authors:

Boboc Nicu Bucur Gheorghe

Affiliation:

(1) Faculty of Mathematics, University of Bucharest, Str. Academiei 14, RO-70109 Bucharest, Romania

Abstract:

We develop the Potential Theory on the set N^* of all natural numbers

2 associated with the kernel V (resp. V^*) given by

$Vf(x) = sumlimits_{mathop {p{text{ prime}}}limits_{p|x} } {f(x/p)} ,{text{ }}V* f(x) = sumlimits_{p{text{ prime}}} {f(xp).}$

We study the extremal elements in the set of all V-supermedian (resp. V^*-supermedian) functions and the Martin boundary of the set N^* associated with V and V^*.

Keywords:

Number thoery potential theory Martin boundary.

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