Montgomery, Hugh L. 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]. Reviewer: Roger Heath-Brown (Oxford) Cited in 3 Documents 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 Keywords:survey; harmonic analysis; analytic number theory; uniform distribution; exponential sums; power sums; irregularities of distribution; large sieve; Dirichlet series; spectral characteristics of zeros of the Zeta-function PDFBibTeX XMLCite \textit{H. L. Montgomery}, NATO Sci. Ser. II, Math. Phys. Chem. 33, 271--293 (2001; Zbl 1001.11001)