Elementary Dirichlet Series and Modular Forms

Elementary Dirichlet Series and Modular Forms By Goro Shimura
English | PDF | 2007 | 151 Pages | ISBN : 0387724737 | 3.03 MB

The main topics of the book are the critical values of Dirichlet L-functions and Hecke L-functions of an imaginary quadratic field, and various problems on elliptic modular forms. As to the values of Dirichlet L-functions, all previous papers and books reiterate a single old result with a single old method. After a review of elementary Fourier analysis, the author presents completely new results with new methods, though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications, new formulas for the second factor of the class number of a cyclotomic field will be given.

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