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- W4311158178 abstract "Different questions lead to the same class of functions from natural integers to integers: those which have integral difference ratios, i.e. verifying $f(a)-f(b)equiv0 pmod {(a-b)}$ for all $a>b$. We characterize this class of functions via their representations as Newton series. This class, which obviously contains all polynomials with integral coefficients, also contains unexpected functions, for instance all functions $xmapstolfloor e^{1/a};a^x;x!rfloor$, with $ainZsetminus{0,1}$, and a function equal to $lfloor e;x!rfloor$ except on 0. Finally, to study the complement class, we look at functions $NtoRR$ which are not uniformly close to any function having integral difference ratios." @default.
- W4311158178 created "2022-12-24" @default.
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- W4311158178 date "2013-10-05" @default.
- W4311158178 modified "2023-10-16" @default.
- W4311158178 title "Newton representation of functions over natural integers having integral difference ratios" @default.
- W4311158178 doi "https://doi.org/10.48550/arxiv.1310.1507" @default.
- W4311158178 hasPublicationYear "2013" @default.
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