We will host the 2021 Zhuhai ANT workshop online from August 24th to 27th, 2021. The organiser and principal contact is Chao Qin.

Talks can be watched through Tencent Meeting ID: 617 6316 4303 You can also enter the meeting room by clicking here.

Aug 24th

9:00--12:00 Shenxing Zhang On the generating fields of Kloosterman sums

14:00--17:00 Di Zhang On the non-vanishing of theta lifts of Bianchi modular forms to Siegel modular forms

9:00--12:00 Yihua Chen Heegner Points on Modular Curves

Aug 25th

14:00--17:00 Zeping Hao

p-adic L-functions in universal deformation families

Aug 26th Aug 27th

9:00--12:00 Jianing Li Revisit Kida's formula in Iwasawa theory

14:00--17:00 Yongxiong Li Quadratic twists of an elliptic curve

9:00--12:00 Shuai Zhai A lower bound result for the 2-part of the Birch-Swinnerton-Dyer exact formula

14:00--17:00 Meng-Fai Lim On order of vanishing of characteristics elements

Yihua Chen -- University of Science and Technology of China

Abstract: In this talk, I will introduce the Heegner points on modular curves, and how to use them to construct the quadratic twist families of Mordell-Weil rank 0 and

1, and some result of BSD formula.

Zeping Hao -- Warwick University

Abstract: In this talk, we construct a two-variable p-adic Rankin-Selberg L- function associated to a pair of modular forms, and discuss its interpolation property. The classical theory of such p-adic L-functions have been studied extensively by Hida in the late 20th century. Recently there has been substantial progress towards different perspectives of this construction. For example, David Loeffler has extended the classical setting (ordinary Hida families) to a more ”arithmetic” one by

allowing the second modular form to vary in universal deformation families, at the expense of restricting tame level to be 1. In this talk I will explain how to relax this tame level condtion, under certain simplifying assumptions imposed solely on the deformation problem.

Jianing Li -- University of Science and Technology of China

Abstract: Kida's formula is about the change of λ-invariants of certain Iwasawa modules, such as S-ramified abelian extension, Selmer groups of elliptic curves and so on, in a Galois p-extension of Zp-fields, under the vanishing of μ-invariants (in general). Here a Zp-field means that it is a finite extension of a cyclotomic (or a Coates-Wiles) Zp-extension. Some results obtained before assume that the prime p is odd. We will also talk about some miscellany about the case p = 2.

Yongxiong Li -- Tsinghua University

Abstract: In this talk, we prove the 2-part of Birch and Swinnerton-Dyer conjecture for an explicit infinite family of rank 0 quadratic twists of the modular elliptic curve X0(14), using an explicit form of the Waldspurger formula. This is joint work with Junhwa Choi.

Meng-Fai Lim -- Central Normal University

Abstract: Let E be an elliptic curve with either good ordinary or split multiplicative reduction at each prime above p. We study the characteristic element of the Selmer group of such an elliptic curve over a p-adic Lie extension. IN particular, we relate the order of vanishing of the characteristic element at certain twist to the Selmer ranks in the intermediate subextension of the said p-adic Lie extension.

Shuai Zhai -- Shandong University

Abstract: In this lecture, we will present a general lower bound for the 2-adic valuation of the algebraic part of the central value of the complex L-series for the quadratic twists of any elliptic curve over the rationals, which shows that when the 2-part of Tamagawa factors is growing, the 2-part of the algebraic central L-value is growing as well, coinciding with the Birch– Swinnerton-Dyer exact formula.

Di Zhang -- Hubei University of Arts and Science

Abstract: In this talk, we study the theta lifting of a weight 2 Bianchi modular form F of level Γ0(n) with n square-free to a weight 2 holomorphic Siegel modular form. Motivated by Prasanna’s work for the Shintani lifting, we define the local Schwartz function at finite places using a quadratic Hecke character χ of square-free conductor f coprime to level n. Then, at certain 2 by 2 Gram matrices related to f, we can express the Fourier coefficient of this theta lifting as a multiple of

L(F, χ, 1) by a non-zero constant. If the twisted L-value is known to be non-vanishing, we can deduce the non-vanishing of our theta lifting.

Shenxing Zhang -- University of Science and Technology of China

Abstract: The arithmetic of exponential sums is a classical topic in number theory. In this talk, we will recall the basic properties of exponential sums, and show how to use l-adic method to obtain the generating fields of general twisted Kloosterman sum.

Huatong Chen Yihua Chen

Haonan Gu Zeping Hao Jianing Li

Yongxiong Li Meng-Fai Lim

Chan Ieong Kuan Didier Lesesvre Evgeny Mayanskiy Chao Qin

Fengpeng Wang Jingyi Xu

Weipeng Yang Dongxi Ye

Miaodan Yuan Shuai Zhai

Di Zhang Shenxing Zhang