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주요 연구 분야

  • 정수론 : Class field theory, Quadratic forms, Modular forms
  • Hilbert’s 12th problem
  • Extended form class groups over number fields
  • Generalized modular forms

교수 주요이력

∙ 現 단국대학교 수학과 부교수, 2020년 3월 1일 ~

∙ 연구교수, 이화여대 수리과학연구소, 2019년 9월 1일 ~ 2020년 2월 28일.

∙ 박사후과정연구원, 이화여대 수리과학연구소, 2019년 8월 1일 ~ 2019년 8월 31일.

∙ 선임연구원, 성균관대학교 AORC, 2017년 8월 1일 ~ 2019년 7월 31일.

∙ 박사후 연구원, 성균관대학교 AORC, 2016년 8월 1일 ~ 2017년 7월 31일.

∙ 박사후 연구원, 국가수리과학연구소, 2014년 8월 1일∼2016년 2월 28일.

∙ 연구조교수, 포항공대 PMI 연구소, 2012년 12월 1일 ~ 2014년 7월 23일.

∙ 박사후 연구원, 포항공대 PMI 연구소, 2012년 9월 1일 ~ 2012년 11월 30일.

∙ 연수연구원, KAIST 자연과학연구소, 2011년 9월 1일 ~ 2012년 8월 31일.

∙ 조교, KAIST 수리과학과, 2007년 봄학기∼2011년 봄학기,

∙ 이학박사, KAIST 수리과학과 석박사 통합과정, 2011년 8월 19일.

∙ 이학사, KAIST 수학과 수학전공, 2005년 2월 18일.

∙ 한성과학고, 2001년 2월 16일.

연구실적

∙ 정호윤, 구자경, 신동화

On some extension of Gauss’work and applications, Open Math., to appear.

∙ 정호윤, 김창헌

Modularity of Galois traces of ray class invariants, Ramanujan J., to appear.

∙ 엄익선, 정호윤, 구자경, 신동화

Composition law and complex multiplication, J. Number Theory, 209 (2020),

396~420.

∙ 엄익선, 정호윤

On some automorphic properties of Galois traces of class invariants from

generalized Weber functions of level 5, Open Math., 17 (2019), 1631~1651.

∙ 정호윤, 김창헌, 권순학, 권영욱

Modularity of Galois traces of Weber’s resolvents, J. Number Theory, 203

(2019), 249~275.

∙ 정호윤, 구자경, 신동화

Primitive and totally primitive Fricke families with applications (II), J. Math.

Anal. Appl., 472 (2019), no. 1, 432~446.

∙ 정호윤, 구자경, 신동화

Generation of ray class fields modulo 2, 3, 4 or 6 by using the Weber function, J.

Korean Math. Soc., 55 (2018), no. 2, 343~372.

∙ 정호윤, 구자경, 신동화

Primitive and totally primitive Fricke families with applications, Results Math.,

71 (2017), issue 3-4, 841~858.

∙ 정호윤, 구자경, 신동화

On some Fricke families and application to the Lang-Schertz conjecture, Proc. R.

Soc. Edinb. Sect. A-Math., 146 (2016), issue 4, 723~740.

∙ 정호윤, 구자경, 신동화,

Application of Weierstrass units to relative power integral bases, Rev. Mat.

Iberoam., 30 (2014), no. 4, 1489~1498.

∙ 정호윤, 구자경, 신동화,

On some arithmetic properties of Siegel functions (II), Forum Math., 26 (2014),

no. 1, 25~57.

∙ 정호윤, 구자경, 신동화,

Normal bases of ray class fields over imaginary quadratic fields, Math. Zeit., 271

(2012), no. 1, 109~116.

∙ 정호윤, 구자경, 신동화,

Ray class invariants over imaginary quadratic fields, Tohoku Math. J., 63 (2011),

no. 3, 413~ 426.

∙ 정호윤, 구자경, 신동화,

Generation of ray class fields by elliptic units, Bull. London Math. Soc., 41

(2009), issue 5, 935~942.

∙ On some extension of Gauss’ work and applications, Canadian Number Theory

Association Conference (CNTA XV), 2018년 7월 11일, 캐나다 라발 대학교.

∙ Generation of ray class fields modulo 2 or 3 by using the Weber function.

International Conference for the 70th Anniversary of Korean Mathematical Society, 2016년 10월 22일, 서울대학교.

∙ Primitive and totally primitive Fricke families with applications.

29th Journees Arithmetiques, 2015년 7월 7일, 헝가리 데브레센 대학교.