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师资力量
蒋玉蛟



教授,博士生导师,山东大学齐鲁青年学者
研究方向:解析数论、自守形式、L-函数

科研项目
[6] 2023.01-2026.12 国家自然科学基金面上项目,国家自然科学基金委,负责人

[5] 2023.01-2025.12 山东省自然科学基金优秀青年基金,山东省自然科学基金委,负责人

[4] 2021.01-2025.12 山东大学(威海)青年学者未来计划,负责人

[3] 2019.01-2021.12 国家自然科学基金青年基金项目,国家自然科学基金委,负责人

[2] 2018.03-2020.12 山东省自然科学基金青年项目,山东省自然科学基金委,负责人

[1] 2017.11-2019.05 中国博士后科学基金面上资助一等资助,中国博士后科学基金会,负责人
学术论文
[31] Y.J. Jiang, T.T Wen and W.J. Zhao. Rational points on a class of cubic hypersurfaces. Forum Math., to appear.

[30] Y.J. Jiang and G.S. Lü. Summation formulae of multiplicative functions over arithmetic progressions and applications. Canad. J. Math., to appear.

[29] Y.J. Jiang and G.S. Lü. Additive divisor problem for multiplicative functions. https://arxiv.org/abs/2204.08221

[28] Y.J. Jiang and G.S. Lü. Correlations of multiplicative functions with automorphic L-functions. Int. Math. Res. Not.,no. 2, 1733-1770, 2024/01.

[27] Y.J. Jiang, G.S. Lü and Z.H. Wang. Möbius randomness law for GL(m) automorphic L-functions twisted by additive characters. Proc. Amer. Math. Soc., 151:475-488, 2023/02.

[26] Y.J. Jiang, G.S. Lü,Z.H. Wang and J. Thorner. A Bombieri-Vinogradov theorem for higher rank groups. Int. Math. Res. Not., no. 1, 482-535, 2023/01.

[25] Y.J. Jiang, G.S. Lü and Z.W. Wang. Averaged form of two conjectures of Erdős and Pomerance, and their applications. Adv. Math., 409, Part A, 108592, 2022/11.

[24] Y.J. Jiang and G.S. Lü. Cancellation in algebraic twisted sums on GL(m). Forum Math., 33(4): 1061-1082, 2021/07.

[23] Y.J. Jiang, G.S. Lü and Z.H. Wang. A Bombieri-Vinogradov theorem for number fields. Mathematika, 67:678-713, 2021/07.

[22] Y.J. Jiang, G.S. Lü and Z.W. Wang. Exponential sums with multiplicative coefficients without the Ramanujan conjecture. Mathematische Annalen, 379:589-632, 2021/02.

[21] Y.J. Jiang and G.S. Lü. The generalized Bourgain-Sarnak-Ziegler criterion and its application to additively twisted sums on GL_m,  SCIENCE CHINA Mathematics, 10:2207-2230, 2021/10.

[20] G.W. Hu, Y.J. Jiang and G.S. Lü. The Fourier coefficients of Theta-series in arithmetic progressions. Mathematika, 66(1):39-55, 2020.

[19] Y.J. Jiang and G.S. Lü. On an analogue of prime vectors among integer lattice points in ellipsoids for automorphic forms, Int. J. Number Theory, 1:145-160, 2020/02.

[18] Y.J. Jiang and G.S. Lü. The Bombieri-Vinogradov theorem on higher rank groups and its applications,  Canad. J. Math., 72(4):928-966, 2020/08.

[17] Y.J. Jiang and G.S. Lü. Quantitative non-vanishing results on L-functions, Quart. J. Math., 70(3):813-830, 2019/09.

[16] Y.J. Jiang, Y.-K. Lau, G.S. Lü, E. Royer and J. Wu. On Fourier coefficients of modular forms of half-integral weight at squarefree integers. Mathematische Zeitschrift, 293:789-808, 2019/10.

[15] Y.J. Jiang and G.S. Lü. Shifted convolution sums for higher rank groups. Forum Math., 31(2): 361–383, 2019/03.

[14] Y.J. Jiang and G.S. Lü. Exponential sums formed with the Möbius function, Indag. Math. (N.S.), 30: 355–364, 2019/03.

[13] Y.J. Jiang and G.S. Lü. On automorphic analogues of the Möbius randomness principle. J. Number Theory, 197: 268–296, 2019/04.

[12] X.G. He and Y.J. Jiang. A note on shifted convolution of cusp-forms with θ-series. Ramanujan J. 47: 1–19,2018.

[11] Y.J. Jiang and G.S. Lü. Oscillations of Fourier coefficients of GL(m) Hecke-Maass forms and nonlinear exponential functions at primes. Funct. Approx. Comment. Math. 57: 185–204,2017.

[10] Y.J. Jiang and G.S. Lü. Exponential sums formed with the von Mangoldt function and Fourier coefficients of GL(m) automorphic forms. Monatsh. Math., 184(4):539–561, 2017.

[9] Y.J. Jiang and G.S. Lü. Fourth power moment of coefficients of automorphic L-functions for GL(m). Forum Math., 29(5): 1199-1212, 2017.

[8] Y.J. Jiang and G.S. Lü. On sums of Fourier coefficients of maass cusp forms. Int. J. Number Theory, 13(05):1233-1243, 2017.

[7] Y.J. Jiang and G.S. Lü. Sums of coefficients of L-functions and applications. J. Number Theory, 171:56-70, 2017.

[6] Y.J. Jiang, G.S. Lü and X.F. Yan. Mean value theorem connected with Fourier coefficients of Hecke-Maass forms for SL(m;Z). Math. Proc. Cambridge Philos. Soc., 161(2):339-356, 2016.

[5] H. Fei, Y.J. Jiang and G.S. Lü. On exponential sums involving coefficients of L-functions for SL(3;Z) over primes. Quart. J. Math., 67(2):285-301, 2016.

[4] Y.J. Jiang and G.S. Lü. Average behavior of Fourier coefficients of Maass cusp forms for hyperbolic 3-manifolds. Monatsh. Math., 178(2):221-236, 2015.

[3] Y.J. Jiang and G.S. Lü. The average order of Hecke eigenvalues of Siegel cusp forms of genus 2. Ramanujan J., 38(3):465-480, 2015.

[2] Y.J. Jiang and G.S. Lü. Uniform estimates for sums of coefficients of symmetric square L-function. J. Number Theory, 148:220-234, 2015.

[1] Y.J. Jiang and G.S. Lü. On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms. Acta Arith., 166(3):231-252, 2014.
联系方式
Email: yujiaoj@sdu.edu.cn
学习经历
2011.09 - 2017.06,山东大学,博士学位 
2007.09 - 2011.06,中国矿业大学,学士学位
访问经历
2015.11 - 2016.11,美国德州农工大学,联合培养博士
在读研究生(以入学时间为序)
硕士研究生:曹丽娟(与孙庆峰教授合带)、张凯炜、张鲲鹏