?

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 2022-11-04
일정종료 2022-11-04
배경색상 #FF5733
  • Date :  2022-11-04 (Fri) 16:00 ~ 17:00
  • Place :  27-325 (SNU)

  • Speaker :  Lee, Seul Bee / 이슬비 (IBS-CGP)
  • Title :  Approximations with mod 2 congruence conditions
  • Abstract :

In the study of Diophantine approximation, a natural question is which rationals p/q minimize |qx-p| with a bounded condition over q. We call such rationals the best approximations. The regular continued fraction gives an algorithm generating the best approximations. From a general perspective, we are interested in the best approximations with congruence conditions on their numerators and denominators. It is known that the continued fraction allowing only even integer partial quotients generates the best approximations whose numerator and denominator have different parity. In this talk, we explain the connection between the best approximations and the Ford circles. Then we explain how we can induce continued fraction algorithms that give the best approximating rationals with congruence conditions of modulo 2. This is joint work with Dong Han Kim and Lingmin Liao.

 

 


List of Articles
No. Subject Author Date Views
Notice QSMS Mailing List Registration qsms 2021.09.09 12034
148 weekplan_672_2020 secret qsms 2020.11.18 0
147 [초청강연 2020.11.27] Zeta함수와 L함수에 대한 역사적 고찰II qsms 2020.11.23 34592
146 [초청강연 2020.11.20] Zeta함수와 L함수에 대한 역사적 고찰 qsms 2020.11.18 6299
145 [정수론 집중강연 2021.08.03, 08.05] Geometric approaches to the local Langlands correspondence I-IV qsms 2021.07.29 4435
144 [사교위상 초청강연 2021.07.16] Categorical entropy and symplectic geometry qsms 2021.07.05 4026
143 [SNU Topology seminar 2024-03-20] Topology of singularities of complex hypersurfaces / The monodromy conjecture for simplicial nondegenerate singularities qsms 2024.03.05 2737
142 [SNU Number Theory Seminiar] 2021.10.15 qsms 2021.09.09 3912
141 [SNU Number Theory Seminiar] 2021.10.08 qsms 2021.08.23 24310
140 [SNU Number Theory Seminiar 2021.11.12] Moduli of Fontaine-Laffailles and mod-p local-global compatibility file qsms 2021.10.29 4073
139 [SNU Number Theory Seminiar 2021.11.05] Bianchi modular symbols and p-adic L-functions qsms 2021.10.20 3801
138 [SNU Number Theory Seminar 6 ~ 7 Feb] Prismatic F-crystals and applications to p-adic Galois representations qsms 2023.02.13 3430
137 [SNU Number Theory Seminar 31 Mar] Height gap theorem and almost law qsms 2023.03.02 3366
136 [SNU Number Theory Seminar 30 June] Do Tropical Markov Cubics dream of Hyperbolic Origami? qsms 2023.06.26 3462
135 [SNU Number Theory Seminar 21 Apr] Selberg's central limit theorem of L -functions near the critical line qsms 2023.04.20 3307
134 [SNU Number Theory Seminar 20220401] Randomness and structure for sums of cubes qsms 2022.03.28 3344
133 [SNU Number Theory Seminar 20220321, 0322, 0324] Three lectures on the Eisenstein ideal qsms 2022.03.19 3358
132 [SNU Number Theory Seminar 2022.03.18] On p-rationality of $\mathbb{Q}(\zeta_{2l+1})^{+}$ for Sophie Germain primes $l$ qsms 2022.03.19 3522
131 [SNU Number Theory Seminar 2022-12-02] Torsion points and concurrent exceptional curves on del Pezzo surfaces of degree one qsms 2022.11.28 3145
130 [SNU Number Theory Seminar 2022-11-11] Mixed moments and the joint distribution of random groups qsms 2022.10.24 3242
» [SNU Number Theory Seminar 2022-11-04] Approximations with mod 2 congruence conditions qsms 2022.10.27 3097
Board Pagination Prev 1 2 3 4 5 6 7 8 Next
/ 8