# Expected value of the smallest denominator in a random interval of fixed radius

@article{Chen2021ExpectedVO, title={Expected value of the smallest denominator in a random interval of fixed radius}, author={Huayang Chen and Alan Haynes}, journal={ArXiv}, year={2021}, volume={abs/2109.12668} }

It has been known since work of Franel [2] and Landau [4] in the 1920’s that the Riemann hypothesis can be reformulated as a question about the distribution of reduced rationals in the unit interval. In light of this, it is perhaps not surprising that the solutions to some basic problems in numerical approximation carry with them a shadow of the Riemann zeta function. Here we address one such problem, which was communicated to us by E. Sander and J. D. Meiss.

#### References

SHOWING 1-8 OF 8 REFERENCES

On the Distribution of Small Denominators in the Farey Series of Order N

- Mathematics
- 2013

Let N be a positive integer. The Farey series of order N is the sequence of rationals h/k with h and k coprime and 1 \(\leq {h} \leq {k} \leq {N} \) arranged in increasing order between 0 and 1, see… Expand

An Introduction to the Theory of Numbers, Sixth Edition

- Mathematics
- 2008

Read more and get great! That's what the book enPDFd an introduction to the theory of numbers 5th edition will give for every reader to read this book. This is an on-line book provided in this… Expand

Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel, Gottinger Nachr

- 1924

Birkhoff averages and rotational invariant circles for area-preserving maps

- Mathematics, Physics
- 2020

Abstract Rotational invariant circles of area-preserving maps are an important and well-studied example of KAM tori. John Greene conjectured that the locally most robust rotational circles have… Expand

Meiss: Birkhoff averages and rotational invariant circles for area-preserving maps

- Phys. D
- 2020

Apostol: Introduction to analytic number theory

- Undergraduate Texts in Mathematics
- 1976

Apostol: Introduction to analytic number theory, Undergraduate Texts in Mathematics

- 1976