Abstract
This paper deals with an application of J. Beck's Fourier transform method for irregularities of distribution on the hyperbolic plane by using a hyperbolic Fourier transform. The discrepancy of a point distribution in a convex set X with respect to hyperbolic circles and with respect to the convex hull of four symmetric points is estimated below. Furthermore it is indicated that these lower bounds are best possible despite of a logarithmic factor.
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References
Beck, J., and W. Chen, “Irregularities of Distribution,” Cambridge University Press, Cambridge-New York, 1987.
Drmota, M., Irregularities of continuous distributions, Ann. Inst. Fourier (3) 39 (1989), 501–527.
Helgason, S., “Topics in Harmonic Anaslysis on Homogeneous Spaces,” Birkhäuser, Boston-Basel-Stuttgart, 1981.
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© 1990 Springer-Verlag
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Drmota, M. (1990). On irregularities of distribution on the hyperbolic plane. In: Hlawka, E., Tichy, R.F. (eds) Number-Theoretic Analysis. Lecture Notes in Mathematics, vol 1452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096979
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DOI: https://doi.org/10.1007/BFb0096979
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