Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis
American Mathematical Soc., 1994 - 220
This volume 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 One particularly valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. The book should be a useful 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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Acta Arith Acta Math Akad apply Approacimation Chapter character mod Conjecture COROLLARY Corput set D(it deduce defined denote the number derive Dirichlet polynomials Erdös estimate exponent pair exponential sum finite follows Fourier Fundamental Lemma Halász Hence Hölder's inequality Hungar hypothesis integral coefficients interval irregularities of distribution J. E. Littlewood L-functions leading coefficient left hand side Littlewood log q 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 Springer-Verlag suffices Suppose Theorem 9 trigonometric polynomial Turán upper bound van der Corput Weyl sums Weyl's criterion zeros zeta function