Department of Mathematics

Liang-Cheng Zhang



Research Interests - Algebraic and Analytic Number Theory

Selected Publications

  1. "Explicit evaluations of two Ramanujan-Selberg continued fractions" International Journal of Number Theory, to appear.
  2. "Explicit evaluation of a Ramanujan-Selberg continued fraction", Proceedings of AMS, 130, No. 1(2001), 9-14.
  3. "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).
  4. "Radicals and units in Ramanujan's work", Acta Arith., LXXXIL.4(1998), pp 145-158 (with Berndt and Chan).
  5. "Ramanujan's class invariants, Kronecker's limit formula and modular equations III", Acta Arith., LXXXII 4 (1997), pp 379-392.
  6. "Ramanujan's association with radicals in India", Amer. Math. Momthly, 104 (Dec., 1997), pp 905-911 (with Bruce Berndt and Chan).
  7. "Ramanujan's remarkable product of Theta functions", Proc. Edinburg Math. Soc., 40 (1997), pp 583-612 (with Berndt and Chan).
  8. "Ramanujan's class invariants, Kronecker's limit formula and modular equations", Trans. Amer. Soc., 349(1997), pp 2125-2173 (with Berndt & Chan).
  9. "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).
  10. "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.
  11. "Explicit values of the Rogers-Ramanujan continued fractions", J.Reine Angew. Math., 480(1996), pp 141-159 (with Berndt and Chan).
  12. "Ramanujan's singular moduli", The Ramanujan Journal,1(1997), pp. 53-74 (with Berndt and Chan).
  13. "Ramanujan's class invariants and cubic continued fractions", Acta, Arith., 73(1995), pp 67-85, (with Berndt and Chan).
  14. "New criterion for class number one for real quadratic fields", Number Theory (CMS Conference Proceedings), Vol. 15, (1995), pp 245-248, (with R. Mollin).
  15. "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)
  16. "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).
  17. "Ramanujan's continued farctions for products of Gamma functions", J. Math. Anal. and Appl., Vol. 174, No. 1, (1993), pp 22-52.
  18. "Orders in quadratic fields II", Proceedings of the Japan Academy, Vol. LXIX, Ser. A, No. 9, (1993), pp 368-371, (with R. Mollin).
  19. "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).
  20. "Ramanujan's identities for eta-functions", Mathematische Annalen, 292 (1992), pp 561-573, (with B. Berndt).
  21. "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).
  22. "q-Difference equations and Ramanujan-Selberg continued fractions", Acta Arith., Vol. 57, No. 4, (1991) pp 307-355.
  23. "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).
  24. "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).
  25. "Some q-integrals associated with modular forms", J. of Math. Anal. and Appl., Vol. 150, No. 1, (1990), pp 264-273.
  26. "On a diophantine equation of Modell in number theory", Acta Sci. of Sichuan Univ., (1990) pp 164-167.
  27. "On the units of cubic and bicubic fields", Acta Math. Sinica, New series, Vol. 1, No. 1, pp 22-34 (1985)
  28. "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.

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