2023 山大数论 π 日

本活动旨在给山大数论方向学生展示和分享自己科研成果的平台，促进数论团队师生的互相了解、共同进步。

报告人 (按姓氏拼音排序)：

华晟昊

李汝森

孙雨田

王鑫

温婷婷

谢思哲

徐晨冉

张慧敏

张晴晴

    

时间：2023-03-14（周二）， 12:00-17:00

地点：明德楼 C704

会议日程：

时间	活动
12:00-13:00	学术交流、活动开幕
13:00-14:00	学术报告：华晟昊、李汝森、孙雨田
14:00-14:15	茶歇
14:15-15:15	学术报告：王鑫、温婷婷、谢思哲
15:15-15:45	茶歇
15:45-16:45	学术报告：徐晨冉、张慧敏、张晴晴
16:45-17:00	自由讨论

报告题目和摘要：

l  报告人：华晟昊

    题目：Extreme central $L$-values of almost prime quadratic twists of  elliptic curves

    摘要：We prove the extreme values of $L$-functions at the central point for almost prime quadratic twists of an elliptic curve. As an application, we get the extreme values for the Tate--Shafarevich groups in the quadratic twist family of an elliptic curve under the Birth--Swinnerton-Dyer conjecture. This is a joint work with Bingrong Huang.

l  报告人：李汝森

    题目：Generalized Alternating Hyperharmonic Numbers

    摘要：We introduced the notion of generalized alternating hyperharmonic numbers and proved that Euler sums of generalized alternating hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.

l  报告人：孙雨田

    题目：Hybrid subconvexity bounds for twist of GL(3) × GL(2) L-functions

    摘要：We give a hybrid subconvexity bound for twists of GL(3)×GL(2) L-functions in the conductor and t aspects, where the conductor is powers of a prime. This is a joint work with Chenchen Shao.

l  报告人：王鑫

    题目：TBA

    摘要：TBA

l  报告人：温婷婷

    题目：Manin's conjecture for singular cubic hypersurfaces

    摘要：Manin's conjecture predicts the quantitative behaviour of rational points on algebraic varieties. For a primitive positive definite quadratic form Q with integer coefficients, the equation x^3 = Q(y)z represents a class of singular cubic hypersurfaces. In this paper, we mainly introduce the distribution of rational points on these hypersurfaces, and describe the ideas, methods, and some results. This is a joint work with Jie Wu and Jianya Liu.

l  报告人：谢思哲

    题目：Two Theorems of Birch for solutions of algebraic equations and their developments

    摘要：Birch's two great theorems, born around 1960, describe solutions of a class of Diophantine equations over Q. It opened up a whole new class of research, and a lot of people made good progress in different aspects based on these two theorems. For example, the solutions of algebraic equations in general number field and the distribution of prime numbers are studied. This talk will give a brief introduction to its developments in recent years.

l  报告人：徐晨冉

    题目：Sign changes of coefficients of half-integral weight Hecke eigenforms

    摘要：Let $\mathfrak{f}$ be a cusp form of half-weight $k+1/2$ and at most quadratic nebentype character whose Fourier coefficients are denoted as $\mathfrak{a}_\mathfrak{f}(n)$. We study sign changes of the family $\{\mathfrak{a}_\mathfrak{f}(tp^2)\}_{p\in\mathbb{P}}$ where $t$ is a square-free number and $p$ runs through the prime numbers.

l  报告人：张慧敏

    题目：On averages of coefficients of L-functions

    摘要：We give proofs of asymptotic formulas for averages of coefficients of degree 5 and degree 7 L-functions whose coefficients can be factorized. Some results by B. Huang, Y. Lin, Q. Sun, Z. Wang and the speaker in this direction will be discussed.

l  报告人：张晴晴

    题目：Roth-type theorem for quadratic equation in Piatetski-Shapiro primes

    摘要：Let $c_1,\dots, c_s$ be nonzero integers satisfying $c_1 + \cdots + c_s = 0$. We consider  the rational quadratic equation $c_1x_1^2 + \cdots + c_s x_s^2 = 0$ where $x_i$ are restricted in subset $\mathcal A$ of Piatetski-Shapiro primes not exceeding $x$ and corresponding to $c$. We show that for $c\in(1,\min\{\frac{s}{s-1},\frac{29}{28}\})$, if the equation has only $K$-trivial solutions in $\mathcal A,$  then {\footnotesize $|\mathcal A| \ll x^{1/c}(\log x)^{-1} (\log \log \log \log x)^{(2-s)/(2c)+\varepsilon}$} holds for $s\geq 7$. This is a joint work with Xiumin Ren and Rui Zhang.

组织者：黄炳荣、林永晓、华晟昊、李良汛

海报：

会议手册：20230314 pi day poster.pdf