LikeN's - a point of view on natural numbers

Edward Tutaj

Abstract


We  define and study  some simple structures which we call  likens and which are conceptually near to both sets of natural numbers, i.e. N with addition and N*=N\{0} with multiplication. It appears, that there are many different likens, which makes it possible to look on usual natural numbers from amore general point of view. In particular, we  show that N and N* are related to some functionals on the  space of likens. A similar idea is known for a long time as  the Beurling generalized numbers. Our approach may beconsidered as a little more natural and more general, since it admits the  finitely generated likens.

Keywords


Beurling numbers; distribution of prime numbers

Mathematics Subject Classification (2010)


11A41

References


Beurling, Arne. "Analyse de la loi asymptotique de la distribution des nombres premiers généralisés. I." Acta Math. 68, no. 1 (1937): 255–291.

Diamond, Harold G., and Wen-Bin Zhang. Beurling generalized numbers. Vol 213 of Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society, 2016.

Ehrhart, Eugène. "Sur les polyèdres rationnels homothétiques à n dimensions." C. R. Acad. Sci. Paris 254 (1962): 616–618.

Rose, Harvey E. A course in number theory. Second edition. New York: The Clarendon Press; Oxford University Press, 1994. Chapter 13.


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