2022.04.19 14:31

# [SNU Number Theory Seminar 2022-05-06] On an upper bound of the average analytic rank of a family of elliptic curves

조회 수 484 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
일정시작 2022-05-06 2022-05-06 #FF5733
• Date :  2022-05-06  (Fri) 16:00

• Place :  27-325 (SNU)

• Speaker :  Keunyoung Jeong (Chonnam National University)
• Title :   On an upper bound of the average analytic rank of a family of elliptic curves
• Abstract;   The average of the rank of elliptic curves over rational numbers in a natural'' family is expected to be 1/2. For example, Goldfeld conjectured that the average of analytic ranks of the quadratic twist family of an elliptic curve over rational numbers is 1/2. In this talk, we will introduce machinery which gives an upper bound of the average of analytic ranks of a family of elliptic curves. To run the machinery, we need to know the probability that an elliptic curve in the family has good/multiplicative/additive reduction (actually we need something more) and use trace formulas. Using the machinery on the set of all elliptic curves over rationals and the set of elliptic curves with a given torsion subgroup respectively, we can compute an upper bound of the n-th moment of the average. This is the first result on an upper bound of the average of the family of elliptic curves with a fixed torsion group, as far as we know. This is joint work with Peter J. Cho.

 제목+내용제목내용댓글이름닉네임아이디태그
List of Articles
번호 제목 글쓴이 날짜 조회 수
공지 QSMS Mailing List Registration 2021.09.09 1159
82 [SNU Number Theory Seminar 2022-06-21] Arithmetic local systems over the moduli space of curves 2022.07.21 372
81 [QSMS Seminar 20220721] Finding ALL solutions 2022.07.14 915
80 [QSMS Mini-course] Pablo Portilla cuadrado (University of Lille) 2022.07.04 427
79 [QSMS Monthly Seminar] Yokonuma Hecke algebras and invariants of framed links 2022.05.27 417
78 [SNU Number Theory Seminar 2022-06-03] The Coleman conjecture on circular distributions and the equivariant Tamagawa Number conjecture 2022.05.18 525
77 [SNU Number Theory Seminar 2022-05-20] Distribution of Hecke eigenvalues of GL_2 automorphic representations 2022.05.18 404
76 [QSMS Geometry Seminar 2022-05-17, 19] Symplectic Criteria on Stratified Uniruledness of Affine Varieties and Applications 2022.05.09 478
75 [QSMS Geometry Seminar 2022-05-12] Tropical Lagrangian multi-sections and tropical locally free sheaves 2022.05.07 462
74 [2022 KMS Spring Meeting] Related talks 2022.04.28 490
73 [QSMS Monthly Seminar] Quantization of integrable differential difference equations 2022.04.22 443
» [SNU Number Theory Seminar 2022-05-06] On an upper bound of the average analytic rank of a family of elliptic curves 2022.04.19 484
71 [SNU Number Theory Seminar 2022-05-13] A singular function containing all Lagrange numbers less than three 2022.04.12 451
70 [SNU Number Theory Seminar 2022-04-15] A note on non-ordinary primes for some genus-zero arithmetic groups 2022.04.12 426
69 [QSMS-BK21 Toric Geometry Seminar] Moduli Space of Special Lagrangians in the Complement of an Anticanonical Divisor 2022.04.12 533
68 [QSMS Seminar 2022.04.19] Universal objects in vertex algebra theory 2022.04.07 462
67 [SNU Number Theory Seminar 20220401] Randomness and structure for sums of cubes 2022.03.28 427
66 [QSMS Monthly Seminar] The dimension of the kernel of an Eisenstein ideal 2022.03.25 458
65 [SNU Number Theory Seminar 20220321, 0322, 0324] Three lectures on the Eisenstein ideal 2022.03.19 369
64 [SNU Number Theory Seminar 2022.03.18] On p-rationality of $\mathbb{Q}(\zeta_{2l+1})^{+}$ for Sophie Germain primes $l$ 2022.03.19 444
63 [BK21-QSMS Toric Geometry Seminar] The Fredholm regularity of discs 2022.03.14 438
Board Pagination Prev 1 2 3 4 5 6 Next
/ 6