Exponential sums for beginner. - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T12:49:27Z http://mathoverflow.net/feeds/question/65429 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/65429/exponential-sums-for-beginner Exponential sums for beginner. Ravinder 2011-05-19T12:42:58Z 2011-09-13T04:05:36Z <p>What are the good books, online lecture notes or starting material on exponentials sums with applications in number theory for a beginner, apart from N. M. Korobov's book? The book or notes should cover methods of Weyl, van der Corput and Vinogradov, with some details. </p> http://mathoverflow.net/questions/65429/exponential-sums-for-beginner/65434#65434 Answer by arithboy for Exponential sums for beginner. arithboy 2011-05-19T13:46:15Z 2011-05-19T13:46:15Z <p>Maybe you will find something useful in the book of Iwaniec &amp; Kowalski entitled " Analytic Number Theory". Morever, I think Huxley's "Area, Lattice Points and Exponential Sums" is worthwhile to read, which focuses a new method deveploed by Bombieri, Iwaniec, Huxley himself and many other followers. </p> http://mathoverflow.net/questions/65429/exponential-sums-for-beginner/65440#65440 Answer by Felipe Voloch for Exponential sums for beginner. Felipe Voloch 2011-05-19T14:23:32Z 2011-05-19T14:23:32Z <p>Shparlinski has a nice set of lecture notes, aimed at beginners, with a view towards applications: <a href="http://www2.ims.nus.edu.sg/Programs/coding/files/ishpar.ps" rel="nofollow">http://www2.ims.nus.edu.sg/Programs/coding/files/ishpar.ps</a></p> http://mathoverflow.net/questions/65429/exponential-sums-for-beginner/65443#65443 Answer by Helge for Exponential sums for beginner. Helge 2011-05-19T14:45:46Z 2011-05-19T14:45:46Z <p>Ten Lectures on the interface of harmonic analysis and number theory by Hugh Montgomery covers these things (Chapters 2 and 3).</p> http://mathoverflow.net/questions/65429/exponential-sums-for-beginner/65458#65458 Answer by Denis Chaperon de LauziÃ¨res for Exponential sums for beginner. Denis Chaperon de LauziÃ¨res 2011-05-19T17:25:08Z 2011-05-19T17:25:08Z <p>For van der Corput's method and some developpments, including the Bombieri-Iwaniec method, the book of Graham and Kolesnik "Van der Corput's method of exponential sums" is one of the best sources. </p> http://mathoverflow.net/questions/65429/exponential-sums-for-beginner/75273#75273 Answer by KConrad for Exponential sums for beginner. KConrad 2011-09-13T04:05:36Z 2011-09-13T04:05:36Z <p>K. Chandrasekharan, Exponential sums in the development of number theory, pp. 7-26 in Proceedings of the International Conference on Number Theory (Moscow, 1971), Trudy Mat. Inst. Steklov 132 (1973).</p>