Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Wydanie 84
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 One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature.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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Chapter 1 Uniform Distribution
Chapter 2 van der Corput Sets
The Methods of Weyl and van der Corput
Chapter 5 An Introduction to Turáns Method
Chapter 6 Irregularities of Distribution
Chapter 7 Mean and Large Values of Dirichlet Polynomials
Chapter 8 Distribution of Reduced Residue Classes in Short Intervals
Chapter 9 Zeros of LFunctions
Chapter 10 Small Polynomials with Integral Coefficients
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Ten Lectures on the Interface Between Analytic Number Theory and Harmonic ...
Ograniczony podgląd - 1994
Acta Arith Acta Math Akad apply approximation Cauchy's inequality Chapter character mod complex numbers Conjecture COROLLARY Corput set deduce defined denote the number derive Diophantine Diophantine Approximation Dirichlet polynomials Erdos estimate exponent pair Exponential sums finite follows Fundamental Lemma Halasz Hence Hungar hypothesis integral coefficients interval irregularities of distribution J. E. Littlewood L-functions leading coefficient left hand side limsup Littlewood London Math lower bound Main Theorem Mean Value Theorem method mod q Nauk SSSR number of solutions Number Theory obtain polynomial of degree polynomials with integral positive integers prime number problem Proc proof is complete prove R. C. Vaughan real number result Riemann zeta function right hand side Ruzsa sequence set of positive Springer-Verlag suffices Suppose Theorem 9 trigonometric polynomial Turan's upper bound values of Dirichlet van der Corput VK(X Weyl sums Weyl's criterion zeros