Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Wydanie 84American 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 One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature.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. |
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 |
Inne wydania - Wyświetl wszystko
Ten Lectures on the Interface Between Analytic Number Theory and Harmonic ... Hugh L. Montgomery Ograniczony podgląd - 1994 |
Ten Lectures on the Interface between Analytic Number Theory and Harmonic ... Hugh L. Montgomery Ograniczony podgląd - 1994 |
Kluczowe wyrazy i wyrażenia
Acta Arith Akad Cauchy's inequality Chapter character mod complex numbers Conjecture COROLLARY Corput set D(it deduce defined denote the number derive Diophantine Approximation Dirichlet polynomials Erdős estimate exponent pair Exponential sums finite follows Fourier Fundamental Lemma Halász Hence Hölder's inequality Hungar integral coefficients interval irregularities of distribution L-functions leading coefficient left hand side lim sup Littlewood log log log q London Math lower bound Main Theorem Mean Value Theorem method mod q modulus Nauk SSSR number of solutions Number Theory polynomial of degree polynomials with integral positive integers prime number problem Proc prove R. C. Vaughan real number Riemann zeta function right hand side Ruzsa sequence Suppose T₁ Theorem 9 trigonometric polynomial Turán ÛN(k upper bound van der Corput Weyl sums Weyl's criterion zeros zeta function λη Σ Σ