Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Wydanie 84

Przednia okładka
American Mathematical Soc. - 220
This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.

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Spis treści

Chapter 1 Uniform Distribution
1
Chapter 2 van der Corput Sets
17
The Methods of Weyl and van der Corput
39
Vinogradovs Method
65
Chapter 5 An Introduction to Turáns Method
85
Chapter 6 Irregularities of Distribution
109
Chapter 7 Mean and Large Values of Dirichlet Polynomials
125
Chapter 8 Distribution of Reduced Residue Classes in Short Intervals
151
Chapter 9 Zeros of LFunctions
163
Chapter 10 Small Polynomials with Integral Coefficients
179
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Strona 192 - Lachance, EB Saff, and RS Varga, Bounds for incomplete polynomials vanishing at both endpoints of an interval, Constructive approaches to mathematical models (Pittsburgh, 1978), Academic Press, New York, 1979, pp.
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Strona 63 - On van der Corput's method and the zeta-function of Riemann (IV)': Quart. J. of Math. (Oxford), 5 (1934), 98-105. Using this result in (3) we shall have AN < AN'*N*log*N, ie N' > ANflog*N, ie G(T) > AT/\o^T.
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