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Harmonic analysis as found in analytic number theory. (English) Zbl 1001.11001
Byrnes, James S. (ed.), Twentieth century harmonic analysis--a celebration. Proceedings of the NATO Advanced Study Institute, Il Ciocco, Italy, July 2-15, 2000. Dordrecht: Kluwer Academic Publishers. NATO Sci. Ser. II, Math. Phys. Chem. 33, 271-293 (2001).
This is a survey describing some of the many questions in harmonic analysis which have arisen in analytic number theory. The topics discussed are uniform distribution, exponential sums, power sums, irregularities of distribution, the large sieve, Dirichlet series, and spectral characteristics of zeros of the zeta-function. For the entire collection see [Zbl 0972.00019].
MSC:
11-02Research monographs (number theory)
43-02Research monographs (abstract harmonic analysis)
42-02Research monographs (Fourier analysis)
11K70Harmonic analysis and almost periodicity
11K38Irregularities of distribution
11L15Weyl sums
11M06$\zeta (s)$ and $L(s, \chi)$
11N30Turán theory
11N35Sieves