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作者(中文):荷涼凡
作者(外文):Pham, Lan-Huong
論文名稱(中文):某些t-模之半週期的超越性
論文名稱(外文):Transcendence of quasi-periods for certain t-modules
指導教授(中文):張介玉
指導教授(外文):Chang, Chieh-Yu
口試委員(中文):于靖
魏福村
口試委員(外文):Yu, Jing
Wei, Fu-Tsun
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學號:107021710
出版年(民國):110
畢業學年度:109
語文別:英文
論文頁數:23
中文關鍵詞:t-模Drinfeld 模半週期函數
外文關鍵詞:t-modulesDrinfeld modulesquasi-periodic functions
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在 [C13] 這篇論文當中, 考慮秩為 2 的 Drinfeld 模基於 Carlitz 模擴張的 t 模,
Chang 引進了秩為 2 的 Drinfeld 模的第三類週期為此 t 模週期的第二個座標.
在此篇論文中, 我們具體導出了此 t 模的準週期為 Carlitz 模的基本週期, 以及
此 Drinfeld 模的週期, 準週期, 對數, 準對數的代數組合. 接著, 我們利用了
Drinfeld 模的 Legendre 關係以及 Chang-Papanikolas 在 Drinfeld 模週期的
代數獨立性, 我們證明了此 t 模的準週期非零情況下的超越性.
In [C13], Chang introduced periods of the third kind of a rank 2 Drinfeld module as the second coordinate of periods of at-module which is formed by the extension of the Drinfeld module by the Carlitz module. In this thesis, we find the quasi-periods of the t-module explicitly as algebraic combinations of the fundamental period of the Carlitz module, and periods, quasi-periods, logarithms, and quasi-logarithms of the Drinfeld module. Then, using the Legendrerelation for Drinfeld modules and an algebraic independence result of Chang and Papanikolas, we prove the transcendence of quasi-periods of this t-module whenever it is nonzero.
Abstract
Contents
1. Introduction ---------------------------------------------- 2
2. Preliminaries --------------------------------------------- 5
 2.1 Anderson t-module and its quasiperiodic function ------- 5
 2.2 Periods of the third kind ------------------------------ 7
3. Transcendence results ------------------------------------- 10
 3.1 Quasi-periods ------------------------------------------ 10
 3.2 Main result -------------------------------------------- 18
[A86] Anderson. G. W. , t-motives, Duke Math. J. 53, 457{502 (1986)
[BP02] Brownawell, W.D., Papanikolas, M.A. Linear independence of Gamma values in positive characteristic. J. Reine Angew. Math. 549, 91{148 (2002)
[C13] Chang, C.-Y. On periods of the third kind for rank 2 Drinfeld module. Math. Z. 273, 921{933 (2013)
[CP12] Chang, C.-Y., Papanikolas, M.A. Algebraic independence of periods and logarithms of Drinfeld modules. With an appendix by Brian Conrad. J. Am. Math. Soc. 25, 123{150 (2012)
[Dr74] Drinfeld, V.G.: Elliptic modules. Math. USSR-Sb. 23, 561{592 (1974)
[Go96] Goss, D. Basic Structures of Function Field Arithmetic.Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, vol. 35. Springer, Berlin (1996)
[PR03] Papanikolas, M.A., Ramachandran, N.: A Weil-Barsotti formula for Drinfeld modules. J. Number Theory 98, 407{431 (2003)
[Ro02] Rosen M. Number Theory in Function Fields. Graduate Texts in Mathematics 210. Springer, New York (2002)
[T04] Thakur, D.S. Function Field Arithmetic. World Scienti c Publishing, River Edge (2004)
[Yu90] Yu, J. On periods and quasi-periods of Drinfeld modules. Compos. Math. 74, 235{245 (1990)
[W95] Woo, S.S.: Extensions of Drinfeld modules of rank 2 by the Carlitz modules. Bull. Korean Math Soc. 32, 251{257 (1995)
 
 
 
 
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