並列摘要
The 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.
參考文獻
Noboru Aoki: On a refinement of a conjecture of Gross for cyclic
extensions of global fields, Preprint, 2003
David Burns: On relations between derivatives of abelian
Darmon, H.: Thaine's method for circular units and a
conjecture of Gross, Canadian J. Math. 47(1995), 302-317.
延伸閱讀
- Nan, T. T. (2009). 函數體上的算術 [master's thesis, National Taiwan Normal University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0021-1610201315152478
- 周義銘（2006）。有關泛凸函數的Hadamard不等式之研究〔碩士論文，淡江大學〕。華藝線上圖書館。https://doi.org/10.6846/TKU.2006.00621
- Lin, K. P., & Yau, S. S. T. (2013). Yau猜想得出的一個數論猜想. 長庚科技學刊, (18), 53-60. https://doi.org/10.6192/CGUST.2013.6.18.6
- 梅哲、趙學信（2016）。數學家如何提出可行的猜想－用結果、隨機性、類比協助推理。數理人文，(8)，8-22。https://doi.org/10.6851/MSHCM.201604_(8).0005
- Ma, Y., Yu, J., & Wang, Y. (2014). Efficient Recursive Methods for Partial Fraction Expansion of General Rational Functions. Journal of Applied Mathematics, 2014(), 946-963-889. https://doi.org/10.1155/2014/895036