Ten lectures on the interface between analytic number theory and harmonic analysis : Expository lectures from the NSF-CBMS Regional Conference, held at Kansas State University, Manhattan, Kansas, May 22-25, 1990

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 One Valuable Aspect Of The Book Is That It Collects Material That Was Either Unpublished Or That Had Appeared Only In The Research Literature.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.--book Jacket. Ch. 1. Uniform Distribution -- Ch. 2. Van Der Corput Sets -- Ch. 3. Exponential Sums I: The Methods Of Weyl And Van Der Corput -- Ch. 4. Exponential Sums Ii: Vinogradov's Method -- Ch. 5. An Introduction To Turan's Method -- Ch. 6. Irregularities Of Distribution -- Ch. 7. Mean And Large Values Of Dirichlet Polynomials -- Ch. 8. Distribution Of Reduced Residue Classes In Short Intervals -- Ch. 9. Zeros Of L-functions -- Ch. 10. Small Polynomials With Integral Coefficients. Hugh L. Montgomery. Expository Lectures From The Nsf-cbms Regional Conference Held At Kansas State University, Manhattan, May 22-25, 1990--t.p. Verso. Includes Bibliographical References And Index. Focuses on topics in analytic number theory that involve ideas from harmonic analysis. This work is suitable for harmonic analysts interested in moving into research in analytic number theory.