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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:

11-02 Research exposition (monographs, survey articles) pertaining to number theory
43-02 Research exposition (monographs, survey articles) pertaining to abstract harmonic analysis
42-02 Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces
11K70 Harmonic analysis and almost periodicity in probabilistic number theory
11K38 Irregularities of distribution, discrepancy
11L15 Weyl sums
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11N30 Turán theory
11N35 Sieves
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