?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
?

Shortcut

PrevPrev Article

NextNext Article

Larger Font Smaller Font Up Down Go comment Print
Extra Form
일정시작 2021-06-11
배경색상 #FF5733

Date: 06월 11일 (금) 14:30~15:30,

Place: Zoom 838 1595 9158

Speaker : 주장원 (울산대학교)

Title : The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma

 

Abstract:

In this talk, we study the representability of integers as sums of pentagonal numbers. In particular, we prove the ``pentagonal theorem of $63$", which states that a sum of pentagonal numbers represents every non-negative integer if and only if it represents the integers  1, 2, 3, 4, 6, 7, 8, 9, 11, 13, 14, 17, 18, 19, 23, 28, 31, 33, 34, 39, 42, and 63.

We also introduce a method to obtain a generalized version of Cauchy's lemma using representations of binary integral quadratic forms by quaternary quadratic forms, which plays a crucial role in proving the results. This is a joint work with Daejun Kim.

 

 

 


List of Articles
No. Subject Author Date Views
Notice QSMS Mailing List Registration qsms 2021.09.09 299
40 [QSMS Monthly Seminar] Closed orbits and Beatty sequences qsms 2021.06.24 693
» [Seminar 2021.06.11] The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma qsms 2021.05.28 668
38 [QSMS Monthly Seminar] Symmetric functions and super duality qsms 2021.05.28 740
37 [Seminar 2021.06.15, 06.22] Cluster algebras with a view toward the Jacobian conjecture qsms 2021.05.28 838
36 [Seminar 2021.05.28] Ramanujan continued fractions of order sixteen qsms 2021.05.21 761
35 [Seminar 2021.05.18] The coherent-constructible correspondence for toric projective bundles qsms 2021.05.17 475
34 [Seminar 2021.05.13] Convergence of harmonic maps via regular nodes qsms 2021.05.12 355
33 [Seminar 2021.05.14] On some results about non-holomorphic Jacobi forms qsms 2021.05.11 484
32 [QSMS Monthly Seminar] Recoverable lattices qsms 2021.05.07 355
31 [Seminar 2021.05.12] Equivariant symplectic homology qsms 2021.05.06 302
30 [Seminar 2021.05.11] Knotted embeddings qsms 2021.05.06 444
29 [Seminar 2021.05.06] Arithmetic properties of weakly holomorphic modular functions of arbitrary level qsms 2021.05.04 441
28 [2021 KMS Spring Meeting] Related talks qsms 2021.04.30 3760
27 [Seminar 2021.04.16] Hecke system of harmonic Maass functions and applications to modular curves of higher genera qsms 2021.04.19 4760
26 [Seminar 2021.04.02] CM congruence and the derivatives of p-adic L-functions for imaginary quadratic fields qsms 2021.04.19 655
25 [Seminar 05.14, 05.21, 05.28, 06.04] Introduction to derived categories qsms 2021.04.16 15563
24 [Seminar 2021.04.23] Quiver Hecke algebras and unipotent quantum coordinate ring qsms 2021.04.09 759
23 [Seminar 2021.04.29] A realization of type A finite $W$-(super)algebra in terms of (super) Yangian qsms 2021.04.09 1325
22 [Seminar 2021.04.02] Quantum affine analog of Kazhdan-Lusztig positivity for non-simply laced types via simply laced types qsms 2021.03.30 7189
21 [QSMS Monthly Seminar] A survey on symplectic fillings and Milnor fibers of a normal complex surface singularity qsms 2021.03.26 775
Board Pagination Prev 1 2 3 Next
/ 3