Office: MC 5004
Phone: 519-888-4567 ext 47202
Fax: 519-725-0160
Email to Wentang Kuo
Research Interests
I am working on Number Theory (both algebraic and analytic), and Algebra. In particular, I am interested in arithmetic properties of function fields, Drinfeld modules, and Waring's problem.
Teaching
I have taught various undergraduate and graduate courses at Purdue University, National Taiwan University, Queen's University and University of Waterloo over the past twenty years, and supervised more than ten graduate students.
Preprints
W. Kuo and Y.-R. Liu, and Y. Totani, "Sums of Two Squares over F_q[T]," preprint (11 Pages).
D. Sourabhashis, W. Kuo and Y.-R. Liu, "Generalizations of the Erdos-Kac theorem with applications," preprint (38 Pages).
W. Kuo, Y.-R. Liu and X. Zhao, "On the multi-dimensional Hilbert-Kamke systems," preprint (38 pages).
L. Eliott, L. Jain and W. Kuo, "Koblitz's Conjecture for the Drinfeld Module," preprint (20 pages).
D. Sourabhashis, W. Kuo and Y.-R. Liu, "On the distribution of the number of distinct generators of h-free and h-full elements in an abelian monoid," submitted, 37 Pages.
D. Sourabhashis, W. Kuo and Y.-R. Liu, "A subset generalization of the Erdos-Kac theorem over number fields with applications," submitted, 33 Pages.
W. Kuo and Y.-R. Liu, and Y. Totani, "A function field analogue
of Jacobi's theorem on sums of squares and its moments,"
submitted, 15 Pages.
Accepted or Published
D. Sourabhashis, W. Kuo and Y.-R. Liu, "Distribution of omega(n) over h-free and h-full numbers," accepted by International Journal of Number Theory, 23 Pages.
D. Sourabhashis, W. Kuo and Y.-R. Liu, "On the number of prime factors with a given multiplicity over h-free and h-full numbers," Journal of Number Theory, 267 (2025) 176-201.
D. Sourabhashis, E Elma, W. Kuo and Y.-R. Liu, "On the number of irreducible factors with a given multiplicity in function fields," Finite Fields Appl, 92 (2023), Paper No. 102281, 22 pp.
W. Kuo and D. Tweedle, "Artin's conjecture for Drinfeld modules," Algebra and Number Theory, 16 (2022), no. 5, 1025--1070.
W. Kuo, Y.-R. Liu, S. Ribas, and K. Zhou, "The Shifted Turan Sieve Method on Tournament II," Discrete Mathematics 344 (2021), no. 12, Paper No. 112602, 11 pp.
W. Kuo and D. Tweedle, "Cyclicity of Drinfeld modules," Bulletin of London Mathematical Society 53 (2021), no. 5, 1500--1519.
W. Kuo and S. Yamagishi, "Sidon basis in polynomial rings over finite fields," Czechoslovak Mathematical Journal, 71(2021) no. 2, 555--562.
W. Kuo and D. Tweedle, "A Prime analogue Erdos-Pomerance result for Drinfeld modules with arbitrary endomorphisms rings," Proceeding of American Mathematical Society, 148(2020), no. 9, 3733--3747.
E. Eisenstein, L. Jain and W. Kuo, "On extending Artin's conjecture to composite moduli in function fields," Journal of Number Theory, 213(2020), 285--318.
W. Kuo, Y.-R. Liu and X. Zhao, " The asymptotic estimates and Hasse principle for multidimensional Waring's problem," Advances in Mathematics, 353(2019), 1--66.
W. Kuo and W.-L. Sun, "The multiplicative Jordan decomposition in the integral group ring Z[Q_8x C_p]," Journal of Algebra, 534(2019), 16--33.
W. Kuo, Y.-R. Liu, S. Ribas, and K. Zhou, "The Shifted Turan Sieve Method on Tournament," Canad. Math. Bull. 62(2019) no. 3, 841--855.
W. Kuo and S. Yamagishi, "On a problem of Sidon for polynomials over finite fields," Acta Arithmetica, 174 (2016), no. 3, 239--254.
W. Kuo and D. Tweedle, "Primitive Submodules for Drinfeld Modules," Mathematical Proceedings of the Cambridge Philosophical Society, 159 (2015), no. 2, 275--302.
Y.-L. Kuan, W. Kuo and W.-C. Yao, "On an Erdos-Pomerance conjecture for rank one Drinfeld modules," Journal of Number Theory, 157 (2015), 1--36.
W. Kuo, Y.-R. Liu and X. Zhao, "Multi-dimensional Vinogradov-type Estimates in Function Fields," Canad. J. Math., 66 (2014), 844-873.
W. Kuo, "Langlands correspondence on the generic constituents of principal series," Canad. J. Math, 62(2010), no. 1, 94-108.
W. Kuo, "A generalization of the Sato-Tate conjecture," Int. J. Number Theory 5 (2009), no.1, 173-184.
W. Kuo and Y.-R. Liu, "A Carlitz module analogue of a conjecture of Erdos and Pomerance," Trans. Amer. Math. Soc., 361 (2009), 4519-4539.
W. Kuo and Y.-R. Liu, "Cyclicity of finite Drinfeld modules," J. London Math. Soc. 80 (2009), 567-584.
W. Kuo and Y.-R. Liu, "Gaussian laws on Drinfeld modules," Int. J. Number Theory, 7 (2009), 1179--1203.
W. Kuo, "Some computations on Bruhat decompositions," an appendix of Complexity of group actions and stability of root numbers, by
F. Shahidi, Comtemp. Math., 489, Automorphic forms and L-functions II, Local aspects, 277-283, Amer. Math. Soc., Providence, RI, 2009.
W. Kuo, and Y.-R. Liu, "The Erdos-Kac theorem and its generalizations," The anatomy of integers, CRM Proceedings & Lecture Notes, 46 (2008), 209-216.
W. Kuo, "A remark on a modular analogue of the Sato-Tate conjecture," Canad. Math. Bull., 50 (2007), no. 2, 234--242.
W. Kuo, "A non-vanishing theorem on Dirichlet series," C. R. Math. Acad. Sci. Soc. R. Can., 27 (2005), no. 3, 76--83.
W. Kuo, and R. Murty, "On a conjecture of Birch and Swinnerton-Dyer," Canad. J. Math., 57 (2005), no. 2, 328--337.
W. Kuo, and R. Murty, "Summatory functions of elements in Selberg's class," Algebraic groups and arithmetic, 525--538, Tata Inst. Fund. Res., Mumbai, 2004.
W. Kuo, "Summatory functions of elements in Selberg's class II," C. R. Math. Acad. Sci. Soc. R. Can., 25 (2003), no. 2, 55--62.
W. Kuo, "Principal nilpotent orbits and reducible principal series," Represent. Theory, 6 (2002), 127--159 (electronic).
W. Kuo, "Principal nilpotent orbits and reducible principal series," MIT thesis, 2000.
