List of Publications

Journal Papers

  1. Y.Choie and W.Kohnen, A remark on the Ikeda left and local singular series polynomials, to appear in Proceedings of A.M.S., Oct 17, 2007
  2. Y.Choie and Y.Chung, Representations of Binary forms by Quaternary forms, to appear in International Journal of Number Theory, Special Issue for the 72nd birthday of Marvin Knopp (2007) (special issue of M.Knopp's 72nd Birthday, 2007
  3. Y.Choie and O.Richter, A combinatorial characterization of Hilbert Jacobi forms, to appear in Rocky Mountain Journal of Mathematics, 2007
  4. Y.Choie and P.Sol/'e, Brou\'e-Enguehard maps and Atkin-Lehner involutions, European Journal of Combinatorics, online Feb. 2007
  5. Y.Choie, Lichiardopol, Moree, Sole, On Robin's criterion for the Riemann Hypothesis, Journal de Theorie des Nombres de Bordeaux, to appear, 2007
  6. Y.Choie and N.Diamantias, Values of L-functions at integers outside the critical strip, appear in Ramanujan Journal, 2007.
  7. Y.Choie and Olav. Richter, Classification of the space spanned by theta series and applications, Proceeding of AMS, 2007
  8. D.Choi and Y.Choie, On the congruence of Jacobi forms, Mathematische Zeitschrift, (2007) 256, 287-294
  9. Y.Choie and DH.Choi, Weight-dependent congruence properties of modular forms, Journal of Number Theory 122 (2007), no. 2, 301--313
  10. Y.Choie and M.Lee, "Rankin-Cohen brackets on Pseudodifferential operators", JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 326 (2): 882-895 FEB 15 2007
  11. Y.Choie and Y. Chung, Linear Relations of Theta Series of Genera of Quadratic forms, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 325 (2): 1430-1441 JAN 15 2007
  12. Y.Choie, H.Kim and O.Richter, Differential operators on the Hilbert forms, JOURNAL OF NUMBER THEORY 122 (1): 25-36 JAN 2007
  13. D.Choi and Y.Choie, Linear Relations among the Fourier Coefficients of Modular Forms on the Genus Zero Group $\Gamma_0(N)$ and Their Applications, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 326 (1): 655-666 FEB 1 2007
  14. Y.Choie and D.Bump, On derivatives of modular forms of negative weight, Pure and Applied Mathematics Quarterly, Volume 2, No.1 (Special issue: In honor of John H.Coates,Part 1 of 2) 113-135, 2006
  15. Y.Choie and N. Diamantis, Rankin-Cohen brackets on Higher order modular forms, Multiple Dirichlet series, Proceedings of Symposia in Pure Mathematics, Vol 75, 193-201, 2006
  16. Y.Choie and M.Oura, " The joint weight enumerators and Siegel modular forms", Proceedings of American Mathematical Society, Vol. 134, 2711-2718, 2006.
  17. Y.Choie and Y. Chung, Linear Relations of Theta Series of Genera of Ternary forms, Acta Arithmetica, Vol.116(4), 287-298, 2005.
  18. Y.Choie and S.T. Dougherty, " Codes over $\Sigma_{2m}$ and Jacobi forms over the Quaternions", Applicable Algebra in Engineering, Communication and Computing, Vol.15, No 2, 129-147, 2005.
  19. K.Betumiya and Y.Choie, Codes over $F_4$, Jacobi forms and Hilbert-Siegel modular forms over $Q(\sqrt{5})$, European Journal of Combinatorics, Vol.26(5), 629-650 , 2005.
  20. Y.Choie and S. Dougherty, "Codes over Rings, Complex Lattices and Hermitian Modular forms", European Journal of Combinatorics, Vol.26(2), 145-165, 2005.
  21. Y.Choie, EK Jeoung and E.Lee, 'Supersingular hyperellitic curve of genus 2 over finite fields', Applied Math and Computation, Vol.163(2), 565-576, 2005.
  22. Y.Choie and Y.Taguchi, Simple proof of modular identity of theta series, Proc. Amer. Math. Soc. 1935--1939, 2005.
  23. Y.Choie, E.Lee and E.Jeong, "Efficient Identity-based authenticated key agreement protocol from pairings", with E.Lee and E.Jeong, Appl. Math. Comput. 162, 179-188, 2005.
  24. K.Betumiya and Y.Choie, Ozeki Polynomials and Jacobi forms, Ars Combin. 77 , 233--244, 2005.
  25. Y. Choie, W. Kohnen, K.Ono, Linear relations between modular form coefficients and non-ordinary primes. Bull. London Math. Soc. 37 no. 3, 335--341, 2005
  26. Y.Choie and E. Jeoung, Isomorphism classes of elliptic and hyperelliptic curves over finite fields over $\mathbf{F}_{(2g+1)^n}$, Finite Fields and Their Applications, Volume 10, Issue 4 , 583-614, 2004.
  27. Y.Choie and P.Sol\'e, Ternary codes and Jacobi forms, Discrete Math, Vol 281, 81-87, 2004.
  28. Y.Choie and E. Lee, "Implementation of Tate-paring of hyperelliptic curve of genus 2", ICISC, Lecture Note in Computer Science, 2971, 97-111 2004.
  29. K. Betumiya and Y.Choie, "Jacobi forms over totally real fields and TypeII codes over Galois rings GR$(2^m,f)$", {\bf{ European Journal of Combinatorics}}, European Journal of Combinatorics, Vol.25(4), 475-486, 2004.
  30. Y.Choie and W. Kohnen, "Special values of elliptic functions at points of the divisors of Jacobi forms", Proceeding of AMS, Vol.131(11), 3309-3317, 2003.
  31. Y.Choie and W.Kohnen, "On the Petersson norm of certain Siegel modular forms", Ramanujan Journal, Vol.7(1), 47-49 2003.
  32. A.Bonnecaze, Y.Choie, S.Dougherty and P.Sole, "Splitting the Shadow", Discrete Math Journal, Vol. 270, 43-60, 2003.
  33. Y.Choie, S.T. Dougherty and H.Kim, "Complete Joint weight enumerators and Self-Dual codes",IEEE Transactions on Information Theory, Vol 49, 1275-1283, 2003.
  34. Y.Choie and G.Frey, Preface, The 2000 Com2Mac workshop in Cryptography, Discrete Applied Math. 130, 1, 2003
  35. Y.Choie and J.Lee, "Speeding up the scalar multiplication in the Jacobians of Hyperelliptic curves using Frobenius map", Lecture note in Computer Science,Vol.2551, 285-295, 2002
  36. Y.Choie and E.Lee, "Jacobi forms over the totally real number fields and Codes over $F_p$". Illinois Journal of Math, Vol 46(2), 627-643, 2002
  37. Y. Choie and D. Yun, "Isomorphism Classes of Hyperelliptic Curves of Genus 2un over ${F}_{q}",$ Lecture Note in Computer Science, Vol. 2384, 190-202,2002
  38. Y.Choie and P.Sol\'e, "Self-dual codes over ${Z_4}$ and half-integral weight modular forms", Proceeding of A.M.S, Vol.130(11), 3125-3131, 2002.
  39. Y.Choie and W.Eholzer, "Jacobi forms and GRC-algebra, Rocky Mountain Journal of Mathematics", Vol. 31, 1265-1365, 2001.
  40. Y.Choie and P.Sol\'e, " Gleason formula for Ozeki polynomials", Journal of Combinatorial Theory, Series A, Vol.98, 60-73, 2002
  41. Y.Choie and H.Kim, "Codes over $\mathbb{Z}_{2m}$ and Jacobi forms of genus $n$", Journal of Combinatorial Theory-Series A, 95, 335-348, 2001.
  42. Y.Choie and W.Kohnen, "Special values of Koecher-Maass series of Siegel cusp forms",Pacific Journal of Mathematics, Vol. 198, No.2, 373-384, 2001.
  43. Y.Choie and H.Kim, "An analogy of Bol's result on Jacobi and Siegel modular forms" (pdf), Journal of Mathematical analysis and its applications, 257, 79-88, 2001.
  44. Y. Choie and N.Kim, "The Complete weight enumeartor of Type II code over ${ Z}_{2m}$ and Jacobi forms",IEEE, Transaction on Information Theory, Vol 47, 1, 396-399, 2001.
  45. Y.Choie, Morain and P.Sole, "Rankin-Cohen Brackets and Invariant Theory",Journal of Algebraic Combinatorics, Vol.13, No.1, 5-13, 2001
  46. Y.Choie, "Half integral weight Jacobi forms and Heat operator",Manuscripta, 104, 123-135, 2001.
  47. Y.Choie and MH.Lee, "Mixed Siegel modular forms and Special values of Certain Dirichlet series", Monatshefte fur Mathematik, 131, 109-122, 2000.
  48. Y.Choie and H.Kim, "Differential operators and Jacobi forms of several variables", Journal of Number Theory, 82, 40-63, 2000.
  49. Y.Choie and MH. Lee, "Mellin transforms and mixed cusp forms", Canadian Mathematical Bulletin . Vol.42, 263-273,1999.
  50. Y. Choie, "Multilinear differential operators on Siegel modular forms of genus 1 and 2", Journal of Mathematical Analysis and Application, 232, 34-44, 1999.
  51. Y. Choie, "Hecke operator and Pseudo-differential operator", Applied Mathematical Letter\, Vol.11, No. 5, 29-34, 1998.
  52. Y. Choie, "Jacobi forms and Heat operatorII", Illinois Journal of Mathematics, Vol.42, No.2, 179-186, 1998.
  53. Y. Choie and W. Eholzer, "Rankin-Cohen operators of Jacobi and Siegel forms", Journal of Number theory, Vol.68, No.2, 160-177, 1998.
  54. Y. Choie, "Constructions of Mixed automorphic forms", Journal of Austrailan Math. Soc. Series A, 63, No.3, 390-395, 1997.
  55. Y. Choie and W. Kohnen, "Rankin's method on Jacobi forms", ABH Math Seminar Hamburg, $ 67, 307-314$, 1997.
  56. Y. Choie, "Correspondence among Eisenstein series $E_{2,1}(\tau,z), E_{2}(\tau), H_{3/2}(\tau)",$ Manuscripta Mathematica, Vol.$93$, Fasc.$2$, $177-187$, 1997.
  57. Y. Choie, "Jacobi forms and the Heat operator", Mathematische Zeitschrift, 225, No$1, 95-101$, 1997.
  58. Y. Choie, "A short note on the full Jacobi group", Proceedings of A.M.S., Vol $123$ No. $9$, $2625-2628$, 1995.
  59. Y. Choie, H. Kim and M. Knopp, "Construction of Jacobi forms", Mathematische Zeitschrift, 219, 71-76, 1995.
  60. Y. Choie, "Hecke operators on rational period functions on the Hecke groups", Results in Mathematics, Vol.25, 40-49, 1994.
  61. Y.Choie and D. Zagier, "Rational period functions for PSL(2, Z)", Contempory Mathematics, A tribute to Emil Grosswald: Number Theory and Related Analysis, 143, 89-108, 1993.
  62. Y. Choie, S. Kim and CN. Lee, Chaotic dynamics and the geometry of the error surface in neural networks, Physica D, 55, 113-120, 1992.
  63. Y. Choie, Rational period functions, class numbers and Diophantine equations, Journal of Number Theory, Vol. 42, 158-188, 1992.
  64. Y. Choie and A. Parson, Rational period functions and indefinite binary quadratic forms II, Illinois Journal of Mathematics, Vol. 35, No.3, 374-400, 1991.
  65. Y. Choie and A. Parson, Congruence relations and periods of cusp forms for the Hecke groups $G(\sqrt2)$ and $G(\sqrt3)$, Results in Mathematics, Vol.17, 57-77, 1990.
  66. Y. Choie and A. Parson, Rational period functions and indefinite binary quadratic forms I, Mathematische Annalen, 286, 697-707, 1990.
  67. Y. Choie, Rational period functions for the modular group and real quadratic fields, Illinois Journal of Mathematics, vol. 33, N. 3, Fall, 495-529, 1989.

International Procceeding Papers (full version)

  1. K.Betumiya and Y.Choie, Invariant Ring of Clifford-Weil Group, and Jacobi Forms over Totally Real Field, The proceedings of the conference AGCT10, Luminy, France, 2006.
  2. Y.Choie and N. Diamantis, Rankin-Cohen brackets on Higher order modular forms, submitted to Proc of Multiple Dirichlet series, to appear on Symposia in Pure Mathematics, 2006
  3. Y.Choie and W.Kohnen, "Diagonalizing ``bad'' Hecke operators on spaces of cusp forms", Number theory, 23--26, Dev. Math, 15, Springer, New York, 23-26, 2006.
  4. Y.Choie and S.Dougherty, "Codes, Lattices and Modular forms", 2003 IEEE INFORMATION THEORY WORKSHOP, "La Sorbonne", ITW2003, Paris, France, 259-282, 2003.
  5. , Y.Choie, Differential operators and Jacobi forms. Automorphic forms and number theory ,urikaisekikenky-usho Koky=uroku No. 1052 74--80,1998.
  6. T. Poston, CN. Lee, Y. Choie and Y. Kwon, Local minima and back propagation, IJCNN'91, Seattle, July 1991, II 173-II 176.
  7. Y. Choie, Y. Kwon, T. Poston and CN. Lee, On benchmarks for learning algorithm, IJCNN'91, Singapore, Nov. 1991, 723-728.

Domestic Procceeding Papers (full version)

Conference Papaer

Research Project Report

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