陳其誠臺灣大學：數學研究所黃柏嶧Huang, Po-YiPo-YiHuang2007-11-282018-06-282007-11-282018-06-282005http://ntur.lib.ntu.edu.tw//handle/246246/59442The family of Stickelberger elements associated to certain abelian extensions over global rational function fields is represented by a universal polynomial. This result is then used to prove a conjecture of Gross for these Stickelberger elements. Keywords: Stickelberger element, special values of abelian L-functions, Conjecture of Gross, Class numbers.1. Introduction .... 1 2. The Conjecture of Gross .... 4 2.1 The Regulator of Gross .... 4 2.2 The shifting of the basic datum .... 6 3. Example .... 9 3.1 Group ring result .... 9 3.2 An example of n=3 ... 11 4. Universal Polynomials ... 17 4.1 Some combinatorial formulae ... 17 4.2 Representable families ... 18 4.3 Computing theta ... 21317125 bytesapplication/pdfen-US葛羅斯猜想Stickelberger elementspecial values of abelian L-functionsConjecture of GrossClass numbersthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59442/1/ntu-94-D88221001-1.pdf