Research

Selected Publications

• On special values of generators of modular function fields (with Dong Hwa Shin), J. Math. Anal. Appl. 530 (2024), no. 2, Paper No. 127741.

• Form class groups and class fields of CM-fields (with Ho Yun Jung, Ja Kyung Koo and Dong Hwa Shin), Results Math. 78 (2023), no. 1, Paper No. 8, 33 pp.

• On some p-adic Galois representations and form class groups (with Ho Yun Jung, Ja Kyung Koo and Dong Hwa Shin), Mathematika 68 (2022), no. 2, 535-564.

• On Siegel invariants of certain CM-fields (with Ja Kyung Koo, Gilles Robert and Dong Hwa Shin), Ramanujan J. 54 (2021), no. 2, 261-284.

• On the Schertz conjecture (with Ja Kyung Koo), Proc. Edinb. Math. Soc. (2) 62 (2019), no. 3, 837–845.

• Construction of class fields over imaginary biquadratic fields (with Ja Kyung Koo), Indiana Univ. Math. J. 68 (2019), 413-434.

• On a problem of Hasse and Ramachandra (with Ja Kyung Koo and Dong Hwa Shin), Open Math. 17 (2019), no. 1, 131-140

• Generators of Siegel modular function fields of higher genus and level (with Ja Kyung Koo and Dong Hwa Shin), J. Math. Anal. Appl. 472 (2019), no. 1, 447-465.

• Form class groups for extended ring class fields (with Ja Kyung Koo and Dong Hwa shin), J. Number Theory 197 (2019), 13-36.

• Siegel families with application to class fields (with Ja Kyung Koo and Dong Hwa Shin), Proc. Roy. Soc. Edinburgh Sect. A 148 (2018), no. 4, 751-771.

• Generation of Siegel modular function fields of even level, Proc. Amer. Math. Soc. 146 (2018), no. 3, 921-931.

• Generation of ring class fields by eta-quotients (with Ja Kyung Koo and Dong Hwa Shin), J. Korean Math. Soc. 55 (2018), no. 1, 131-146.

• Construction of ray class fields by smaller generators and applications (with Ja Kyung Koo), Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), no. 4, 781-812.

• Normal bases for modular function fields (with Ja Kyung Koo and Dong Hwa Shin), Bull. Aust. Math. Soc. 95 (2017), no. 3, 384-392.

• Generators of the ring of weakly holomorphic modular functions for Gamma_1(N) (with Ja Kyung Koo), Ramanujan J. 42 (2017), no. 3, 583-599.

• Construction of class fields over cyclotomic fields (with Ja Kyung Koo), Kyoto J. Math. 56 (2016), 803-829.

• Generation of class fields by using the Weber function (with Ja Kyung Koo and Dong Hwa Shin), J. Number Theory 167 (2016), 74-87.

• Ray class fields generated by torsion points of certain elliptic curves (with Ja Kyung Koo and Dong Hwa Shin), Ramanujan J. 28 (2012), no. 3, 341–360. 

• Algebraic integers as special values of modular units (with Ja Kyung Koo and Dong Hwa Shin), Proc. Edinb. Math. Soc. (2) 55 (2012), no. 1, 167-179.

• Representations by x_1^2+2x_2^2+x_3^2+x_4^2+x_1x_3+x_1x_4+x_2x_4 (with Ick Sun Eum and Dong Hwa Shin), J. Number Theory 131 (2011), 2376-2386.

Submitted Papers

• Gauss' form class groups and Shimura's canonical models (with Ja Kyung Koo and Dong Hwa Shin), submitted.

• Class fields and form class groups for solving certain quadratic Diophantine equations (with Ho Yun Jung, Ja Kyung Koo and Dong Hwa Shin), submitted.

• Arithmetic properties of orders in imaginary quadratic fields (with Ho Yun Jung, Ja Kyung Koo and Dong Hwa Shin), submitted.

• (title undecided, something about Robert invariants) (with Gilles Robert), in preparation.

• (title undecided, something about Hilbert class fields over CM-fields), in preparation.

Talks

• [May 2024] Number Theory Seminar at Chonnam National University, Online (Korea). 

  • Class fields and form class groups for solving certain quadratic Diophantine equations

• [May 2021] Yonsei math seminar 2021, Online (Korea).

  • On Siegel invariants of certain CM-fields

• [Feb. 2019] Annual number theory workshop 2019, Seoul (Korea).

  • Form class groups for extended ring class fields

• [June 2018] MPI-Oberseminar, Bonn (Germany).

  • Construction of class fields over CM-fields

• [Aug. 2017] UNIST Number Theory seminar, Ulsan (Korea).

  • Generators of Siegel modular function fields of higher genus and level

• [Dec. 2016]  5th Meeting of Young Number Theorists, Seoul (Korea).

  • Hasse-Ramachandra's problem

• [Aug. 2016] CTNT 2016 Conference on elliptic curves, modular forms, and related topics (USA).

  • Generators of Siegel modular function fields of higher genus and level

• [Feb. 2016] The 5th Number Theory Festival, Changwon (Korea).

  • Generators of Siegel modular functions of higher genus

• [July. 2015]  The 29th Journées Arithmétiques JA2015, Debrecen (Hungary).

  • Siegel invariant and its application

• [June. 2015]  4th Meeting of Young Number Theorists, Seoul (Korea).

  • Applications of modular units

• [Apr. 2015]  2015 KMS Spring Meeting, Busan (Korea).

  • Generation of the ring of weakly holomorphic modular functions for Gamma_1(N)

• [Oct. 2014]  2014 KMS Annual Meeting, Seoul (Korea).

  • Generation of class fields by using the Weber function

• [June. 2014] 13th Conference of the Canadian Number Theory Association, Ottawa (Canada).

  • Construction of class fields over imaginary biquadratic fields

• [June. 2014] NIMS PostDoc. Seminar, Daejeon (Korea).

  • Hilbert's 12th problem

• [Apr. 2014] 2014 KMS Spring Meeting, Gangneung (Korea).

  • Ring class fields by smaller generators

• [Nov. 2013] PMI T-seminar, Pohang (Korea).

  • Hilbert's 12th problem

• [Oct. 2013] KIAS Number Thoery Seminar, Seoul (Korea).

  • Construction of class fields over imaginary biquadratic fields

• [Oct. 2013] 제3회 수학문화축전 (3rd Mathematics Culture Festival), Gwacheon (Korea).

  • 소수란 무엇인가 (What is a prime number)

• [Aug. 2013] NIMS Pure and Applied Number Theory Conference, Daejeon (Korea).

  • Construction of class fields over imaginary biquadratic fields

• [July. 2013] The 28th Journées Arithmétiques JA2013, Grenoble (France).

  • Construction of class fields over imaginary biquadratic fields

• [Feb. 2013] The 2nd Number Theory Festival, Seoul (Korea).

  • Construction of class fields over cyclotomic fields

• [Apr. 2012] 2012 KMS Spring Meeting, Seoul (Korea).

  • Some application of the complex multiplication of abelian varieties

• [Oct. 2010] 2010 Global KMS International Conference, Pohang (Korea).

  • Algebraic integers as special values of modular units

• [Dec. 2009] Joint Meeting of the Korean Mathematical Society and the American Mathematical Society, Seoul (Korea).

  • Ray class fields generated by torsion points of certain elliptic curves

• [Aug. 2009] KIAS Number theory Seminar, Seoul (Korea).

  • Ray class fields generated by torsion points of certain elliptic curves