楊一帆(Yi-Fan Yang)特聘教授兼理學院副院長
聯絡方式
- Email: yfyang@math.nctu.edu.tw
- 電話: 03-571-2121 ext. 56419
- 傳真: 03-572-4679
- 地址: 新竹市大學路1001號 交通大學 應用數學系
- 相關網站:
近兩學期教授課程
- 112 學年度第一學期:
- 機率論
- 112 學年度第二學期:
- 離散數學專題(二)
- 數論與密碼學
履歷
- 學歷
- 伊利諾大學香檳分校數學系博士
- 台灣大學數學系學士
- 學術專長暨研究領域
- 數論
- 學術經歷與榮譽
- 伊利諾大學香檳分校數學系Bateman Prize in Number Theory(2000-2001)
- 高等研究院博士後研究 (2000-2001)
- 國立新加坡大學 Research Fellow (2001-2003)
- 國立交通大學應用數學系助理教授 (2003-2005)
- 國立交通大學應用數學系副教授 (2005-2009)
- 國立交通大學應用數學系教授 (2009-)
- 國立交通大學理學院學士班主任 (2011-)
- 中央研究院年輕學者著作獎(2006)
- 中華民國數學學會青年數學家獎(2007)
- 吳大猷先生紀念獎(2008)
- 科技部傑出研究獎(2014)
- 國科會數學學門審議委員 (2013-)
- 台灣數學期刊 (Taiwanese Journal of mathematics)編輯 (2013-)
- 近五年研究計劃
- 志村曲線上的自守型式及其相關問題 (NSC 102-2115-M-009-001-MY4)
- 分割數函數,志村對應,四元theta函數及L-函數的特殊值 (99-2115-M-009-011-MY3)
- 卡拉比—邱流型與齊苟模型式的關聯(3/3) (98-2115-M-009-001)
- 卡拉比—邱流型與齊苟模型式的關聯(2/3) (97-2115-M-009-001)
- 卡拉比—邱流型與齊苟模型式的關聯(1/3) (96-2628-M-009-014)
- 賈可比式, 模式, 類數, 及多變數zeta函數的研究(2/2)(95-2115-M-009-005-)
- 賈可比式, 模式, 類數, 及多變數zeta函數的研究(1/2)(94-2115-M-009-012-)
- 模曲線之定義方程式, cusp型, 及其相關問題(93-2115-M-009-014- )
- 虧格為零之SL_2(Z)同餘子群(92-2119-M-009-001- )
- 指導研究生
研究生博士班:
陳耀漢(99畢)
凃芳婷(102畢)
郭家瑋(103畢)
林易萱(在學)研究生碩士班:
李仁豪(94畢)
凃芳婷(95畢)
林家銘(99畢)
黃彥璋(99畢)
林易萱(100畢)
施建宏(102畢)
周孝賢(在學)
劉又齊(在學)
研究趣向
數論
著作選集
(A) Refereed Papers:
1. Yifan Yang, partitions into primes, Trans. Amer. Math. Soc., 352 (2000), 2581—2600.
2. Yifan Yang, inverse problems for partition functions, Canad. J. Math. 53 (2001), 866—896
3. Yifan Yang, on a multiplicative partition function, Electron. J. Combin. 8 (2001) Research Paper 19, 14pp.
4. Yifan Yang, on differential equations satisfied by modular forms, Math. Z. 246 (2004), 1—19.
5. Yifan Yang, transformation formulas for generalized Dedekind eta functions, Bull. London Math. Soc. 36 (2004), 671—682.
6. Yifan Yang, on integrals of Eisenstein series and derivatives of L-series, Int. Math. Res. Not., 2004, 303—307.
7. Kok Seng Chua, Mong Lung Lang, Yifan Yang, on Rademacher’s conjecture: congruence subgroups of genus zero of the modular group, J. Algebra 277 (2004), 408—428.
8. Ling Long and Yifan Yang, a short proof of Milne’s formulas for sums of integer squares, Int. J. Number Theory 1 (2005) 533—551.
9. Yifan Yang, defining equations of modular curves, Adv. Math. 204 (2006) 481—508.
10. Hung-Jen Chiang-Hsieh and Yifan Yang, determination of Hauptmoduls and construction of abelian extensions of quadratic number fields, Canad. Math. Bull. 50 (2007), 334—346.
11. Noriko Yui and Yifan Yang, differential equations satisfied by modular forms and K3 surfaces, Illinois J. Math. 51 (2007), 667—696.
12. Yao-Han Chen, Yifan Yang, and Noriko Yui, monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds, J. Reine Angew. Math. 616 (2008) 167—203.
13. Yifan Yang, Apery limits and special values of L-functions, J. Math. Anal. Appl. 343 (2008), 492—513.
14. Yifan Yang, on the mean square of the Riemann zeta function and the divisor problems, Publ. Inst. Math. (Beograd), 83 (2008), 71—86.
15. Shinji Fukuhara and Yifan Yang, period polynomials and explicit formulas for Hecke operators on Gamma_0(2), Math. Proc. Cambridge Philos. Soc., 146 (2009), 321—250.
16. Fang-Ting Tu and Yifan Yang, defining equations of X_0(2^{2n}), Osaka J. Math, 46 (2009), 105—113.
17. Yifan Yang, modular units and cuspidal divisor class groups of X_1(N), J. Algebra, 322 (2009), 514—553.
18. Aristides Kontogeorgis and Yifan Yang, automorphism groups of hyperelliptic modular curves, LMS J. Comp. Math. 13 (2010), 144—163.
19. Yifan Yang and Jeng-Daw Yu, structure of the cuspidal rational torsion subgroups of J_1(p^n), J. London Math. Soc 82 (2010), 203—228.
20. Shinji Fukuhara and Yifan Yang, twisted Hecke L-values and period polynomials, J. Number Theory 130 (2010), 976—999.
21. Yifan Yang and Wadim Zudilin, an Sp_4 modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds, Contemporary Mathematics 517, 381—413.
22. Yifan Yang, congruences of the partition function, Int. Math. Res. Not., 2011, 3261—3288.
23. Heng Huat Chan, Ling Long, and Yifan Yang, a cubic analogue of the Jacobsthal identity, Amer. Math. Monthly 118:4 (2011), 316—326.
24. Heng Huat Chan, Yoshio Tanigawa, Yifan Yang, and Wadim Zudilin, new analogues of Clausen’s identities arising from the theory of modular forms, Adv. Math 228 (2011), 1294-1314.
25. Shinji Fukuhara and Yifan Yang, a basis for and representations of integers as sums of squares, Ramanujan J. 28 (2012), 25—43.
26. Ki-Ichiro Hashimoto, Ling Long, and Yifan Yang, Jacobsthal identity for Q(sqrt(-2)), Forum Math. 24 (2012) , 1225—1238.
27. Fang-Ting Tu and Yifan Yang, lattice packing from quaternion algebras, RIMS Kokyuroku Bessatsu B32 (2012), 229—237.
28. Yifan Yang, Schwarzian differential equation and automorphic forms on Shimura curves, Compositio Math. 149 (2013), 1—31.
29. Fang-Ting Tu and Yifan Yang, algebraic transformations of hypergeometric functions and automorphic forms on Shimura curves, Trans. Amer. Math. Soc. 365 (2013), 6697—6729.
30. Shinji Fukuhara and Yifan Yang, a basis for and formulas for even powers of the Jacobi theta function, Int. J. Number Theory 9 (2013), 1973—1993.
31. Yifan Yang, modular forms of half-integral weights on SL(2,Z), Nagoya J. Math. 215 (2014), 1—66.
32. Yifan Yang, Ramanujan-type identities for Shimura curves, Israel J. Math., to appear (2015).
- Yifan Yang, computing modular equations for Shimura curves, preprint.
- Yifan Yang, special values of hypergeometric functions and periods of CM elliptic curves, submitted.
- Jia-Wei Guo and Yifan Yang, equations of Shimura curves, submitted.
- Yi-Hsuan Lin and Yifan Yang, quaternionic loci in Siegel’s modular threefold, in preparation.
(C) Others:
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