조회 수 1917 추천 수 0 댓글 0
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
?

단축키

Prev이전 문서

Next다음 문서

크게 작게 위로 아래로 댓글로 가기 인쇄
Extra Form
일정시작 2021-05-28
일정종료 2021-05-28
배경색상 #FF5733

Date:  5월 28일 (금) 15:30~16:30

Place:  Zoom (ID: 818 0514 4375)

Speaker : 박윤경 (서울과학기술대학교)

Title: Ramanujan continued fractions of order sixteen

 

Abstract:

We study the continued fractions $I_1(\tau)$ and $I_2(\tau)$ of order sixteen by adopting the theory of modular functions. These functions are analogues of Rogers--Ramanujan continued fraction $r(\tau)$ with modularity and many interesting properties. Here we prove the modularities of $I_1(\tau)$ and $I_2(\tau)$ to find the relation with the generator of the field of modular functions on $\Gamma_0(16)$. Moreover we prove that the values $2(I_1(\tau)^2 + 1/I_1(\tau)^2)$ and $2(I_2(\tau)^2+1/I_2(\tau)^2)$ are algebraic integers for certain imaginary quadratic quantity $\tau$.

 

 

 

 

 


List of Articles
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration qsms 2021.09.09 2461
122 [QSMS Monthly Seminar] A survey on symplectic fillings and Milnor fibers of a normal complex surface singularity qsms 2021.03.26 1484
121 [Seminar 2021.04.02] Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types qsms 2021.03.30 8050
120 [Seminar 2021.04.29] A realization of type A finite $W$-(super)algebra in terms of (super) Yangian qsms 2021.04.09 2474
119 [Seminar 2021.04.23] Quiver Hecke algebras and unipotent quantum coordinate ring qsms 2021.04.09 1749
118 [Seminar 05.14, 05.21, 05.28, 06.04] Introduction to derived categories qsms 2021.04.16 16503
117 [Seminar 2021.04.02] CM congruence and the derivatives of p-adic L-functions for imaginary quadratic fields qsms 2021.04.19 1809
116 [Seminar 2021.04.16] Hecke system of harmonic Maass functions and applications to modular curves of higher genera qsms 2021.04.19 5582
115 [2021 KMS Spring Meeting] Related talks qsms 2021.04.30 4765
114 [Seminar 2021.05.06] Arithmetic properties of weakly holomorphic modular functions of arbitrary level qsms 2021.05.04 1372
113 [Seminar 2021.05.11] Knotted embeddings qsms 2021.05.06 1189
112 [Seminar 2021.05.12] Equivariant symplectic homology qsms 2021.05.06 1100
111 [QSMS Monthly Seminar] Recoverable lattices qsms 2021.05.07 1031
110 [Seminar 2021.05.14] On some results about non-holomorphic Jacobi forms qsms 2021.05.11 1264
109 [Seminar 2021.05.13] Convergence of harmonic maps via regular nodes qsms 2021.05.12 1228
108 [Seminar 2021.05.18] The coherent-constructible correspondence for toric projective bundles qsms 2021.05.17 1330
» [Seminar 2021.05.28] Ramanujan continued fractions of order sixteen qsms 2021.05.21 1917
106 [Seminar 2021.06.15, 06.22] Cluster algebras with a view toward the Jacobian conjecture qsms 2021.05.28 2001
105 [QSMS Monthly Seminar] Symmetric functions and super duality qsms 2021.05.28 1608
104 [Seminar 2021.06.11] The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma qsms 2021.05.28 1598
103 [QSMS Monthly Seminar] Closed orbits and Beatty sequences qsms 2021.06.24 1603
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8