2026年合肥数论研讨会
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HefeI Number Theory Seminar (HINTS) 2026
会议信息
| 报告时间： | 2026年3月21日~22日 |
| 报告地点： | 中国科学技术大学第五教学楼5307 (21日)、5107 (22日) |
| 主办单位： | 中国科学技术大学数学科学学院 |
| 合肥工业大学数学学院 | |
| 组委会： | 欧阳毅 中国科学技术大学 |
| 杨金榜 中国科学技术大学 | |
| 张神星 合肥工业大学 | |
| 吴小胜 合肥工业大学 | |
| 会务联系： | 张神星 zhangshenxing@hfut.edu.cn |
| 杨金榜 yjb@ustc.edu.cn |
报告安排
| 3月21日 10:00~10:45 曹炜 (闽南师范大学) Value sets of multivariate polynomial We extend the nullity for a finite 1-tuple multiset to a finite 𝑚-tuple multiset, and then use it to give an upper bound for the value set of a multivariate polynomial over the multisets drawn from a field. Our results generalize and refine two generalizations of original Wan's upper bound for the value set of a univariate polynomial in finite fields. |
| 3月21日 11:00~11:45 洪绍方 (四川大学) Proofs of Lupu's conjectures for multiple zeta values and multiple 𝑡-values Let 𝑟≥1 be an integer. For any multiple index 𝑠=(𝑠1,𝑠2,…,𝑠𝑟)∈ℤ𝑟≥1 with 𝑠𝑟>1, the multiple zeta value (MZV for short) is defined by 𝜁(𝑠1,𝑠2,…,𝑠𝑟):=Σ_{1≤k1<k2<…<k𝑟} 𝑘1−𝑠_1 𝑘2−𝑠_2 … 𝑘𝑟−𝑠_𝑟 and the multiple 𝑡-value is defined by 𝑡(𝑠1,𝑠2,…,𝑠𝑟):=Σ_{1≤k1<k2<…<k𝑟} (2𝑘1−1)−𝑠_1(2𝑘2−1)−𝑠_2… (2𝑘𝑟−1)−𝑠_𝑟 where if the index is empty, then we define the value 𝑡(∅):=1. We denote by {𝑎1,…,𝑎𝑘}𝑑 the sequence formed by repeating the sequence {𝑎1,…,𝑎𝑘} exactly 𝑑 times. Let 𝐻(𝑎,𝑏)=𝜁({2}𝑎,3,{2}𝑏>) and 𝑇(𝑎,𝑏):=𝑡({2}𝑎,3,{2}𝑏). In this talk, by using the Lai-Lupu-Orr integral expressions for 𝐻(𝑎,𝑏) and 𝑇(𝑎,𝑏) and the properties of Beta function and Gamma function, we show that for any nonnegative integers 𝑎 and 𝑏, we have 𝐻(𝑎,𝑏):=(−4𝜋2𝑎+2𝑏+2)/(2𝑎+2)! Σ∞𝑛=0 𝜁(2𝑛)/(2𝑛+2𝑎+2)(2𝑛+2𝑎+3)…(2𝑛+2𝑎+2𝑏+3)22𝑛 and 𝑇(𝑎,𝑏)=−2/(2𝑎+1)!(𝜋/2)2𝑎+2𝑏+2 Σ∞𝑛=0 𝜁(2𝑛)/(2𝑛+2𝑎+1)(2𝑛+2𝑎+2)…(2𝑛+2𝑎+2𝑏+2)22𝑛. This confirms two conjectures of Lupu proposed in 2022. This talk is based on a joint work with Drs. W.Z. Lei and J.M. Yu. |
| 3月21日 14:30~15:15 李吉有 (上海交通大学) Improving bounds for value sets of polynomials over finite fields Let 𝔽𝑞 be a finite field of characteristic 𝑝, and let 𝑓(𝑥)∈𝔽𝑞[𝑥] be a polynomial of degree 𝑑>0. Let 𝑁𝑓 be the cardinality of the image set of 𝑓(𝑥) on 𝔽𝑞. In this talk, we present a new bound for 𝑁𝑓. In particular, for any 𝑝≠2,3, and for every generic quartic polynomial 𝑓, we obtain a sharper bound 𝑁𝑓−5𝑞/8 ≤√𝑞/2+3/4, which holds as a simple corollary of the main result. Joint work with Zhiyao Zhang. |
| 3月21日 15:30~16:15 祝辉林 (厦门大学) Applications of Diophantine approximation to Sun Zhi-Wei's conjecture about difference between powers In this talk we will answer a part of Sun Zhi-Wei’s conjecture by solving some kind of Generalized Ramanujan-Nagell Equation. In order to obtain the result we will recall some development in this direction. In fact we may research some related Diophantine equations to approach another part of Sun's conjecture. |
| 3月21日 16:30~17:15 周海港 (同济大学) Explicit computation of Fourier coefficients of Siegel Eisenstein series of degree two In this talk, for Siegel modular forms of degree two weight two, we construct a basis of its subspace of Siegel Eisenstein series of square-free level 𝑁, and compute their Fourier coefficients explicitly. In addition, we connect the theta series from Yoshida lifting associated to Eichler orders with Siegel Eisenstein series. |
| 3月22日 09:00~09:45 秦厚荣 (南京大学) The CM conductor and the Lang-Trotter Conjecture for CM elliptic curves For an elliptic curve 𝐸 with complex multiplication (CM) defined over ℚ, we introduce a new invariant, the CM conductor 𝒦𝐸, which refines the Serre conductor in the CM case. Using 𝒦𝐸, we give a corrected formula for the constant 𝑐𝐸,𝑟 in the Lang-Trotter conjecture, which predicts an asymptotic formula 𝜋𝐸,𝑟(𝑥)~ 𝑐𝐸,𝑟>√𝑥/log 𝑥 for 𝜋𝐸,𝑟(𝑥)=#{𝑝≤𝑥 : 𝑎𝑝=𝑟}, where 𝑎p is the Frobenius trace of 𝐸 at a prime 𝑝 of good reduction and 𝑟≠0 is a fixed integer. This corrected formula differs from the one previously suggested by Baier and Jones (which was based on the Serre conductor). Assuming the Hardy-Littlewood conjecture on the number of primes represented by quadratic polynomials, we prove that our version of the Lang-Trotter conjecture holds for every CM elliptic curve defined over ℚ. Moreover, we compute the density constants explicitly for each imaginary quadratic field of class number one, and provide extensive numerical evidence that strongly supports our formulation. This is joint work with Longxi Hu and Kaisheng Lei. |
| 3月22日 10:00~10:45 郭学军 (南京大学) 同余数椭圆曲线的𝐿-函数中心值 设 𝐸𝑛 为同余数椭圆曲线 𝑦2=𝑥3−𝑛2𝑥，其中 𝑛 无平方因子且不被模 4 余 3 的素数整除。我们证明 𝐿(𝐸𝑛, 1) 可以表示为 Dirichlet theta 函数在 CM 点处取值的平方，从而推广了 Gauss 的两个经典公式。该工作与叶东曦和尹洪波合作完成。 |
| 3月22日 11:00~11:45 袁平之 (华南师范大学) Ko’s method and its applications In this talk, we will talk about the well-known method on Diophantine equations–Ko’s method. In particular, we will present some applications of Ko’s method to some famous Diophantine equations. [1] Yuan Pingzhi, Li Yuan. Squares in Lehmer sequences and the Diophantine equation 𝐴𝑥4−𝐵𝑦2=2. Acta Arith. 139 (2009), no. 3, 275–302. [2] Luo Jiagui, Yuan Pingzhi. Square-classes in Lehmer sequences having odd parameters and their applications. Acta Arith. 127 (2007), no. 1, 49–62. [3] Yuan Pingzhi, Luo Jiagui. On the Diophantine equation (𝑥2±𝐶)(𝑦2±𝐷)=𝑧4. Acta Arith. 144 (2010), no. 1, 69–95. |