Department of Mathematics
Liang-Cheng Zhang
Professor
Education
- B.S. and M.S in Math, Peking(Beijing) University, China
- Ph. D. in Math, University of Illinois at Urbana-Champaign
Research Interests - Algebraic and
Analytic Number Theory
- Class Invariants and Singular Moduli
- Class Ideal Groups and Class Numbers of Quadratic Fields
- Unit Groups of Number Fields
- Class Field Theory, Genus Theory and Complex Multiplication
- Continued Fractions
- Elliptic Functions and Modular Forms
- q-Series
- Diophantine Equations
- Ramanujan's Work
Selected Publications
- "Explicit evaluations of two Ramanujan-Selberg continued fractions"
International Journal of Number Theory, to appear.
- "Explicit evaluation of a Ramanujan-Selberg continued fraction",
Proceedings of AMS, 130, No. 1(2001), 9-14.
- "A certain quotient of eta-functions found in Ramanujan's Lost
Notebooks, Pacific Journal of Mathematics,Vol. 202, No. 2
(2002), pp 267-304 (with Berndt,
Chan and Kang).
- "Radicals and units in Ramanujan's work", Acta Arith.,
LXXXIL.4(1998), pp 145-158 (with Berndt and Chan).
- "Ramanujan's class invariants, Kronecker's limit formula and modular
equations III", Acta Arith., LXXXII 4 (1997), pp 379-392.
- "Ramanujan's association with radicals in India", Amer. Math.
Momthly, 104 (Dec., 1997), pp 905-911 (with Bruce Berndt and Chan).
- "Ramanujan's remarkable product of Theta functions", Proc.
Edinburg Math. Soc., 40 (1997), pp 583-612 (with Berndt and Chan).
- "Ramanujan's class invariants, Kronecker's limit formula and modular
equations", Trans. Amer. Soc., 349(1997), pp 2125-2173 (with
Berndt & Chan).
- "Ramanujan's class invariants with applications to the values of
q-continued fractions and Theta functions", Fields Institute
Communications, 14(1997), pp37-53 (with Berndt and Chan).
- "Ramanujan's class invariants, Kronecker's limit formula and modular
equations II", Analytic Number Theory, Proceedings of Conference in Honor of
H. Halberstam, Birhauser, (1996), Vol. 2, pp 817-838.
- "Explicit values of the Rogers-Ramanujan continued fractions", J.Reine
Angew. Math., 480(1996), pp 141-159 (with Berndt and Chan).
- "Ramanujan's singular moduli", The Ramanujan
Journal,1(1997), pp. 53-74 (with Berndt and Chan).
- "Ramanujan's class invariants and cubic continued fractions", Acta, Arith.,
73(1995), pp 67-85, (with Berndt and Chan).
- "New criterion for class number one for real quadratic fields", Number
Theory (CMS Conference Proceedings), Vol. 15, (1995), pp 245-248, (with
R. Mollin).
- "A lower bound for the class number of a real quadratic field of
ERD-type",
Canadian Mathematical Bulletin, Vol. 37 (1994), pp 90-96, (with R. Mollin
& P.Kemp)
- "A new class of theta function identities originating in Ramanujan's
Notebooks", Journal of Number Theory, Vol. 48, No. 2,(1994), pp 224-242,
(with Berndt).
- "Ramanujan's continued farctions for products of Gamma functions", J.
Math. Anal. and Appl., Vol. 174, No. 1, (1993), pp 22-52.
- "Orders in quadratic fields II", Proceedings of the Japan Academy, Vol.
LXIX, Ser. A, No. 9, (1993), pp 368-371, (with R. Mollin).
- "Reduced ideals, the divisor function, continued fractions and class
numbers of real quadratic fields", Publicationes Mathematicae,
Debrecen, Tomus 43/3-4, (1993), pp 315-328, (with R. Mollin).
- "Ramanujan's identities for eta-functions", Mathematische Annalen, 292
(1992), pp 561-573, (with B. Berndt).
- "On unit solution of the equation xyz=x+y+z in total imaginary
quartic fields", Journal of Number Theory, Vol. 40, No. 3 (1992), pp 255-263,
(with H. Edgar and J. Gordon).
- "q-Difference equations and Ramanujan-Selberg continued fractions",
Acta
Arith., Vol. 57, No. 4, (1991) pp 307-355.
- "On unit solutions of the equation xyz=x+y+z in not total real cubic
fields", Canadian Math. Bulletin, Vol. 34(1), (1991), pp 141-144,
(with J. Gordon).
- "On unit solution of the equation xyz=x+y+z in a number field with
unit group of rank one", Acta Arith., Vol. 57, No. 2, (1991),
pp 155-158, (with J. Gordon).
- "Some q-integrals associated with modular forms", J. of Math. Anal.
and Appl., Vol. 150, No. 1, (1990), pp 264-273.
- "On a diophantine equation of Modell in number theory", Acta Sci. of
Sichuan Univ., (1990) pp 164-167.
- "On the units of cubic and bicubic fields", Acta Math. Sinica, New series,
Vol. 1, No. 1, pp 22-34 (1985)
- "On a principle of reduction of fields Q(cubic root of m_1, ..., cubic
root of m_r)", Advances in Math (Chinese), Vol. 12, No.3 (1983),
PP 237-240.
Favourite Activities
Contact Information
- Email: liz917f@missouristate.edu
- Department of Mathematics
Missouri State University
Springfield, MO 65897
- Phone: (417)836-5230
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Liang-Cheng
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