## Linear independence of dilogarithmic values.(English)Zbl 1454.11131

Summary: We establish the linear independence over $$\mathbb{Q}$$, in both qualitative and quantitative forms, of the four numbers 1, $$\operatorname{Li}_{1}(1/z)=-\log(1-1/z)$$, $$\operatorname{Li}_{2}(1/z)$$ and $$\operatorname{Li}_{2}(1/(1-z))$$, for all integers $$z\geq9$$ or $$z\geq8$$ and for rationals $$z=s/r$$ or $$z=1-s/r$$ with $$1<r<s$$, where $$s$$ is large in comparison with $$r$$.

### MSC:

 11J72 Irrationality; linear independence over a field 11J82 Measures of irrationality and of transcendence
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### References:

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