Erdős Problem #989 — Circle discrepancy for planar point sequences

About 62 years old · traced to

For an infinite planar point sequence AA, let f(r)=max⁡C∣∣A∩C∣−πr2∣f(r)=\max_C ||A∩C|-πr^2|, with the maximum over circles of radius rr. Must f(r)f(r) be unbounded, and how fast must it grow?

References

Additional references

P. Erdős, Problems and results on diophantine approximations, Compositio Mathematica 16 (1964), 52–65.

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