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Xiumin Ren

Email: xmren@sdu.edu.cn

Address: School of Mathematics

Shandong University

Jinan, Shandong 250100, China

Personal Homepage

Education

Ph.D.: Shandong University, 2001

M.S.: Capital Normal University, 1987

B.S.: Hebei Normal University, 1984

Professional Positions

2004- present: Full Professor, Shandong University

2001-2004: Post-Doctoral Fellow, University of Hong Kong

1997-2004: Associate Professor, Shandong University

1995-1997: Lecturer, Shandong University

1987-1995: Lecturer, Ningxia University

Research Interests

Additive number theory, Exponential sums and Automorphic forms 

Grants

2019-2022: National natural science foundation (Grant No. 11871307), by the National natural science foundation.

2016-2020: Member of the Key Project of National Natural Foundation (Grant No.11531008), by the National Natural Science Foundation.

2015-2017: Shandong province natural science foundation (Grant No. ZR2015-AM016), by the Shandong province natural science foundation.

2010-2012: National natural science foundation (Grant No. 10971119), by the National natural science foundation.

2006-2008: National natural science foundation.

2004-2006: Foundation for the distinguished young scholars of Shandong province.

Publications

[24] (with Qingqing Zhang and Rui Zhang) Roth-type theorem for quadratic system in Piatetski-Shapiro primes. J. Number Theory, 257 (2024), 123.

[23] (With Wei Zhang) Averages of exponential twists of the von Mangoldt function. Bull. Aust. Math. Soc. 106 (2022), no. 3, 425–430.

[22] (With Wei Zhang) On sums of biquadratic powers with almost equal primes. Ramanujan J. 57 (2022), no. 1, 71–78.

[21] (With Wei Zhang) Zero-density estimate of L-functions for cusp forms. J. Number Theory 194 (2019), 284–296.

[20] (with Yangbo Ye) Hyper-Kloosterman sums of different moduli and their applications to automorphic forms for SLm(Z). Taiwanese J. Math. 20 (2016), no. 6, 1251–1274.

[19] (with Yangbo Ye) Resonance and rapid decay of exponential sums of Fourier coefficients of a Maass form for GLm(Z). Sci. China Math. 58 (2015), no. 10, 2105–2124.

[18] (with Yangbo Ye) Resonance of automorphic forms for GL(3). Trans. Amer. Math. Soc. 367 (2015), no. 3, 2137–2157.

[17] (with Yangbo Ye) Sums of Fourier coefficients of a Maass form for SL3(Z) twisted by exponential functions. Forum Math. 26 (2014), no. 1, 221–238.

[16] (with Yangbo Ye) Asymptotic Voronoi's summation formulas and their duality for SL3(Z). Number theoryarithmetic in ShangriLa, 213–236.

[15] (with Kui Liu) On exponential sums involving Fourier coefficients of cusp forms. J. Number Theory 132 (2012), no. 1, 171–181.

[14] (with Yangbo Ye) Resonance between automorphic forms and exponential functions. Sci. China Math. 53 (2010), no. 9, 2463–2472.

[13] (with Kaiman Tsang) Waring-Goldbach problems for unlike powers. II. Acta Math. Sinica (Chinese Ser.) 50 (2007), no. 1, 175–182.

[12] (with Kaiman Tsang) Waring-Goldbach problem for unlike powers. Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 2, 265–280.

[11] Vinogradov's exponential sum over primes. Acta Arith. 124 (2006), no. 3, 269285.

[10] (with Kaiman Tsang) On representation of integers by sums of a cube and three cubes of primes. Michigan Math. J. 53 (2005), no. 3, 571–577.

[9] On exponential sums over primes and application in Waring-Goldbach problem. Sci. China Ser. A 48 (2005), no. 6, 785–797.

[8] (with Kaiman Tsang) On Roth's theorem concerning a cube and three cubes of primes. Q. J. Math. 55 (2004), no. 3, 357–374.

[7] (with Kaiman Tsang) On a Waring-Goldbach-type problem for fourth powers. J. Number Theory 108 (2004), no. 1, 90–110.

[6] The major arcs in the ternary Goldbach problem. Acta Math. Hungar. 98 (2003), no. 12, 39–58.

[5] Sums of four cubes of primes. J. Number Theory 98 (2003), no. 1, 156–171.

[4] Density of integers that are the sum of four cubes of primes. Chinese Ann. Math. Ser. B 22 (2001), no. 2, 233–242.

[3] The exceptional set in Roth's theorem concerning a cube and three cubes of primes. Q. J. Math. 52 (2001), no. 1, 107–126.

[2] The Waring-Goldbach problem for cubes. Acta Arith. 94 (2000), no. 3, 287–301.

[1] Newton-like methods for determining zeros of nonsmooth order-convex operators. Numer. Math. J. Chinese Univ. 15 (1993), no. 3, 232–239.