Shen, Li-Chien

• 3878804
  Shen, Li Chien(1-FL)
  Department of Mathematics, University of Florida
  Gainesville, Florida, 32611
  On Schwarzian triangle functions, automorphic forms and a generalization of Ramanujan's triple differential equations. (English summary)
  Acta Math. Sin. (Engl. Ser.) 34 (2018), no. 11, 1648-1662.
  33C75
  
• 3820866
  Shen, Li-chien(1-FL)
  Department of Mathematics, University of Florida
  Gainesville, Florida, 32611
  On Eisenstein series generated from twisting of the geometric series. (English, Chinese summary)
  J. East China Norm. Univ. Natur. Sci. Ed. 2017, no. 6, 1-24.
  33E30
  
• 3581603
  Shen, Li Chien(1-FL)
  Department of Mathematics, University of Florida
  Gainesville, Florida, 32611
  On three differential equations associated with Chebyshev polynomials of degrees 3, 4 and 6. (English summary)
  Acta Math. Sin. (Engl. Ser.) 33 (2017), no. 1, 21-36.
  33C75 (34A05)
  
• 3581603
  Shen, Li Chien(1-FL)
  Department of Mathematics, University of Florida
  Gainesville, Florida, 32611
  On three differential equations associated with Chebyshev polynomials of degrees 3, 4 and 6. (English summary)
  Acta Math. Sin. (Engl. Ser.) 33 (2017), no. 1, 21-36.
  33C75 (34A05)
  
• 3472128
  Shen, Li-Chien(1-FL)
  On Hecke groups, Schwarzian triangle functions and a class of hyper-elliptic functions. (English summary)
  Ramanujan J. 39 (2016), no. 3, 609-638.
  33C75
  
• 3206196
  Shen, Li-Chien(1-FL)
  On a theory of elliptic functions based on the incomplete integral of the hypergeometric function ${}_2F_1(\frac{1}{4},\frac{3}{4};\frac{1}{2};z)$${}_2F_1(\frac{1}{4},\frac{3}{4};\frac{1}{2};z)$. (English summary)
  Ramanujan J. 34 (2014), no. 2, 209-225.
  33C75
  
• 3017926
  Shen, Li-Chien(1-FL)
  A note on Ramanujan's identities involving the hypergeometric function ${}_2F_1(\frac{1}{6},\frac{5}{6};1;z)$${}_2F_1(\frac{1}{6},\frac{5}{6};1;z)$. (English summary)
  Ramanujan J. 30 (2013), no. 2, 211–222.
  33C75
  
• 2471616
  Shen, Li-Chien(1-FL)
  On the points of order 3 of the period parallelogram of the Weierstrass elliptic function. (English summary)
  Ramanujan J. 18 (2009), no. 1, 61--72.
  33Exx (11L05)
  
• 2407068
  Shen, Li-Chien(1-FL)
  On separation of quadratic forms on the imaginary quadratic field in its Hilbert class field. (English summary)
  Proc. Amer. Math. Soc. 136 (2008), no. 9, 3061--3067.
  11E25
  
• 2115090
  Shen, Li-Chien(1-FL)
  On the theory of elliptic functions based on $\sb 2F\sb 1({1\over3},{2\over3};{1\over2};z)$. (English. English summary)
  Trans. Amer. Math. Soc. 357 (2005), no. 5, 2043--2058 (electronic).
  11Lxx
• 2022370
  Shen, Li-Chien(1-FL)
  On a class of elliptic functions associated with imaginary quadratic fields. (English. English summary)
  Proc. Amer. Math. Soc. 132 (2004), no. 2, 463--471 (electronic).
  11R11 (11R29)
• 1896410
  Rao, Murali(1-FL); Shen, Li-Chien(1-FL)
  Application of the Borel transform to the study of the spectrum of integral equations whose kernels are entire functions of exponential type. (English. English summary)
  Proc. Amer. Math. Soc. 130 (2002), no. 8, 2287--2294 (electronic).
  45E10 (31A10 44A20 47G10)
• 1883404
  Shen, Li-Chien(1-FL)
  On polynomial approximation of square integrable functions on a subarc of the unit circle. (English. English summary)
  J. Approx. Theory 114 (2002), no. 2, 152--163.
  41A10 (41A63)
• 1855619
  Shen, Li-Chien(1-FL)
  On some inequalities involving the zeros and weighted $L\sp p$ norms of polynomials. (English. English summary)
  Proc. Amer. Math. Soc. 130 (2002), no. 1, 53--57 (electronic).
  30C10 (30C15 41A17)
• 1815296
  Shen, Li-Chien(1-FL)
  Reproducing kernels and some associated extremal problems of analytic functions in the unit disc. (English. English summary)
  Adv. Stud. Contemp. Math. (Pusan) 3 (2001), no. 1, 59--70.
  30C40
• 1802005
  Shen, Li-Chien(1-FL)
  Orthogonal polynomials on the unit circle associated with the Laguerre polynomials. (English. English summary)
  Proc. Amer. Math. Soc. 129 (2001), no. 3, 873--879 (electronic).
  33C47 (42C05)
• 1738901
  Shen, Li-Chien(1-FL)
  On the products of three theta functions. (English. English summary)
  Ramanujan J. 3 (1999), no. 4, 343--357.
  33D15 (11F27)
• 1633743
  Shen, Li-Chien(1-FL)
  On a class of $q$-series related to quadratic forms. (English. English summary)
  Bull. Inst. Math. Acad. Sinica 26 (1998), no. 2, 111--126.
  11L03 (11R11 33D10)
• 1617305
  Shen, Li-Chien(1-FL)
  On an identity of Ramanujan based on the hypergeometric series $\sb 2F\sb 1(\frac 13,\frac 23;\frac 12; x)$. (English. English summary)
  J. Number Theory 69 (1998), no. 2, 125--134.
  11F27 (33C05 33E05)
• 1473599
  Shen, Li-Chien(1-FL)
  A note on the Schwarzian triangle functions. (English. English summary)
  Complex Variables Theory Appl. 34 (1997), no. 1-2, 187--196.
  33C05
• 1273524
  Shen, Li-Chien(1-FL)
  On some modular equations of degree $5$. (English. English summary)
  Proc. Amer. Math. Soc. 123 (1995), no. 5, 1521--1526.
  33D10 (11B65)
• 1257124
  Shen, Li-Chien(1-FL)
  Remarks on some integrals and series involving the Stirling numbers and $\zeta(n)$. (English. English summary)
  Trans. Amer. Math. Soc. 347 (1995), no. 4, 1391--1399.
  11B73 (11M06 11Y60 33C05)
• 1250827
  Shen, Li-Chien(1-FL)
  On the additive formulae of the theta functions and a collection of Lambert series pertaining to the modular equations of degree $5$. (English. English summary)
  Trans. Amer. Math. Soc. 345 (1994), no. 1, 323--345.
  33D10 (11F27)
• 1212287
  Shen, Li-Chien(1-FL)
  On the modular equations of degree $3$. (English. English summary)
  Proc. Amer. Math. Soc. 122 (1994), no. 4, 1101--1114.
  11F27 (33E05)
• 1189748
  McCullough, Scott(1-FL); Shen, Li-Chien(1-FL)
  On the Szegö kernel of an annulus. (English. English summary)
  Proc. Amer. Math. Soc. 121 (1994), no. 4, 1111--1121.
  30C40 (46E22)
• 1186995
  Shen, Li-Chien(1-FL)
  On a definite integral of a hypergeometric function. (English. English summary)
  Proc. Amer. Math. Soc. 120 (1994), no. 4, 1131--1136.
  33C75
• 1224821
  Shen, Li-Chien(1-FL)
  On the logarithmic derivative of a theta function and a fundamental identity of Ramanujan.
  J. Math. Anal. Appl. 177 (1993), no. 1, 299--307.
  11F27 (11F11 11M06)
• 1152291
  Shen, Li-Chien(1-FL)
  On some cubic modular identities.
  Proc. Amer. Math. Soc. 119 (1993), no. 1, 203--208.
  11F03
• 1132424
  Shen, Li-Chien(1-FL)
  On the zeros of the solutions of $y"+P(z)y=0$ where $P(z)$ is a polynomial.
  Proc. Amer. Math. Soc. 117 (1993), no. 4, 1057--1061.
  34A20 (30D20)
• 1109575
  Shen, Li-Chien(1-FL)
  On the zeros of $\tan\sp {(k)}z$.
  Amer. Math. Monthly 98 (1991), no. 6, 524--527.
  30C15
• 1039265
  Shen, Li-Chien(1-FL)
  Comments on an $L\sp 2$ inequality of A. K. Varma involving the first derivative of polynomials.
  Proc. Amer. Math. Soc. 111 (1991), no. 4, 955--959.
  26D15
• 915718
  Shen, Li-Chien(1-FL)
  On the area of the region where an entire function is greater than one.
  Proc. Amer. Math. Soc. 102 (1988), no. 1, 68--70.
  30D15 (30D20)
• 894428
  Shen, Li-Chien(1-FL)
  Zeros of successive derivates of a class of real entire functions of exponential type.
  Proc. Amer. Math. Soc. 100 (1987), no. 4, 627--634.
  30D20 (30C15)
• 884470
  Shen, Li-Chien(1-SRCS)
  Proof of a conjecture of Bank and Laine regarding the product of two linearly independent solutions of $y"+Ay=0$.
  Proc. Amer. Math. Soc. 100 (1987), no. 2, 301--308.
  34A20 (30D35)
• 877043
  Rao, Murali(1-FL); Shen, Li-Chien(1-FL)
  On the final set of a real entire function of exponential type.
  Proc. Amer. Math. Soc. 99 (1987), no. 4, 700--704.
  30D15 (30D40)
• 860385
  Shen, Li-Chien(1-SRCS)
  On the zeros of successive derivatives of even Laguerre-Pólya functions.
  Trans. Amer. Math. Soc. 298 (1986), no. 2, 643--652.
  30D15 (30C15)
• 850643
  Shen, Li-Chien(1-SRCS)
  Solution to a problem of S. Bank regarding exponent of convergence of zeros of the solutions of differential equation $f"+Af=0$.
  Kexue Tongbao (English Ed.) 30 (1985), no. 12, 1579--1585.
  34A20 (30D20)
• 809952
  Shen, Li-Chien(1-CAIT)
  Influence of the distribution of the zeros of an entire function and its second derivative on the growth of the function.
  J. London Math. Soc. (2) 31 (1985), no. 2, 305--320.
  30D15 (30C15)
• 810160
  Shen, Li-Chien(1-SRCS)
  Construction of a differential equation $y"+Ay=0$ with solutions having the prescribed zeros.
  Proc. Amer. Math. Soc. 95 (1985), no. 4, 544--546.
  34A20 (30D20)
• 752502
  Hellerstein, Simon(1-WI); Shen, Li-Chien(1-CAIT); Williamson, Jack(1-HI)
  Real zeros of derivatives of meromorphic functions and solutions of second order differential equations.
  Trans. Amer. Math. Soc. 285 (1984), no. 2, 759--776.
  30D35 (34A20)
• 730036
  Hellerstein, Simon(1-WI); Shen, Li-Chien(1-CAIT); Williamson, Jack(1-HI)
  Solutions with only real zeros of second order differential equations and zeros of derivatives of a meromorphic function.
  Value distribution theory and its applications (New York, 1983), 63--67,
  Contemp. Math., 25,
  Amer. Math. Soc., Providence, RI, 1983.
  34A20 (30D30 30D35)
• 725651
  Shen, Li Jian(1-CAIT)
  On classification of meromorphic functions by the zeros of their derivative.
  Sci. Sinica Ser. A 26 (1983), no. 8, 825--834.
  30D30 (30D35)
• 678353
  Hellerstein, Simon; Shen, Li Chien; Williamson, Jack
  Reality of the zeros of an entire function and its derivatives.
  Trans. Amer. Math. Soc. 275 (1983), no. 1, 319--331.
  30D20 (30D30 30D35)
• 467371
  Allen, G. D.; Shen, L. C.
  On the structure of principal ideals of operators.
  Trans. Amer. Math. Soc. 238 (1978), 253--270.
  47B05 (47D99)