Academic Webs

Distinguished Professor and Associate Dean of College of Science Yi-Fan Yang

Contact

Email: yfyang@math.nctu.edu.tw
Tel: +886-3-571-2121 ext. 56419
Fax: +886-3-572-4679
Address: Department of Applied Mathematics, National Chiao Tung University,1001 Ta Hsueh Road, Hsinchu, Taiwan 30050, ROC

Teaching

Fall Semester, 2024：
- Probability Theory

Spring Semester, 2024：
- Topics in Discrete Maths.(II)
- Number Theory and Cryptography

Vitae

Education
- Ph.D. in mathematics, University of Illinois at Urbana-Champaign
- B.S. in mathematics, National Taiwan University

Research Areas
- Number Theory

Positions, Honors and Awards

Recent Research Projects
- Automorphic forms on Shimura curves and their related problems -- Yi-Fan Yang (NSC 102-2115-M-009-001-MY4)
- Partition Function, Shimura Correspondence, Quaternary Theta Series, and Special Values of L-Functions (99-2115-M-009-011-MY3)
- Differential equations of Calabi-Yau type and Siegel modular forms(3/3) (98-2115-M-009-001)
- Differential equations of Calabi-Yau type and Siegel modular forms(2/3) (97-2115-M-009-001)
- Differential equations of Calabi-Yau type and Siegel modular forms(1/3) (96-2628-M-009-014)
- On Jacobi forms, modular forms, class numbers, and multiple zeta functions (2/2) (NSC 95-2115-M-009-005-)
- On Jacobi forms, modular forms, class numbers, and multiple zeta functions (1/2) (NSC 94-2115-M-009-012-)
- Defining equations of modular curves, cusp forms, and other related problems (NSC 93-2115-M-009-014- )
- Genus zero congruence subgroups of (NSC 92-2119-M-009-001- )

Selected Publications

(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.

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