Research Areas: Number Theory

  gslv@sdu.edu.cn

Ph.D.: Shandong University, 2004

M.S.: Shandong Normal University, 2001  

B.S.: Shandong Normal University, 1998

2023.09—: Special Support Plan for National High Level Talents

2017.12—: Taishan Scholar, Shandong Province

2009.12—: Full Professor, Shandong University

2007.12-2009.01: Postdoc, Stanford University

2006.09-2009.12: Associate Professor, Shandong University

2004.07-2006.09: Assistant Professor, Shandong University

2. The second prize of the state natural science award, by the State Council of the People's Republic of China, 2014.

1. The first-class award of natural sciences, by the Ministry of Education of the People's Republic of China, 2011.

[106] (With Q. Ma), Exponential sums with the Dirichlet coefficients of Rankin–Selberg L-functions, Monatsh. Math., 204(2024), 127-155.

[105] (With Y.J. Jiang), Correlations of multiplicative functions with coefficients of automorphic L-functions, Int. Math. Res. Not. IMRN, 2024, no. 2, 1733-1770.

[104] (With Q. Ma), Monotone chains in modulus of two classes of Dirichlet coefficients, Acta Math. Sin. (Engl. Ser.), 39(2023), 1101-1114.

[103] (With Y.J. Jiang), A survey on coefficients of automorphic L-functions, Adv. Math. (China), 52(2023), 201-223.
[102] (With Y. Jiang, J. Thorner, Z. Wang), A Bombieri-Vinogradov theorem for higher-rank groups, Int. Math. Res. Not. IMRN, 2023, no. 1, 482-535.

[101] (With Y.J. Jiang, Z.H. Wang), Möbius randomness law for GL(m) automorphic L-functions twisted by additive characters, Proc. Amer. Math. Soc., 151(2023), 475-488.

[100] (With G.W. Hu), Jutila's circle method and GL(2)×GL(2) shifted convolution sums, J. Number Theory, 242(2023), 709-724.

[99] (With Y.J. Jiang, Z.W. Wang), Averaged forms of two conjectures of Erdős and Pomerance, and their applications, Adv. Math., 409(2022), part A, Paper No. 108592, 42 pp.

[98] (With G.W. Hu), Shifted convolution sums of GL(m) cusp forms with Θ-series, Ramanujan J., 56(2021), 555-584.

[97] (With Y.J. Jiang), The generalized Bourgain-Sarnak-Ziegler criterion and its application to additively twisted sums on GL_{m}, Sci. China Math., 64(2021), 2207-2230.

[96] (With Y.J. Jiang), Cancellation in algebraic twisted sums on GL_{m}, Forum Math., 33 (2021), 1061-1082.

[95] (With Y.J. Jiang, Z.H. Wang), A Bombieri-Vinogradov theorem for number fields, Mathematika, 67(2021), 678-713.

[94] (With Y.J. Jiang, Z.W. Wang), Exponential sums with multiplicative coefficients without the Ramanujan conjecture, Math. Ann., 379 (2020), 589-632.

[93] (With G.W. Hu), Sums of higher divisor functions, J. Number Theory, 220(2021), 61-74.

[92] (With G.W. Hu), Shifted convolution sums for SL(m), Manuscripta Math., 163(2020), 375-394.

[91] (With G.W. Hu, Y.J. Jiang), The Fourier coefficients of Θ-series in arithmetic progressions, Mathematika, 66(2020), 39-55.

[90] (With Y.J. Jiang), The Bombieri-Vinogradov theorem on higher rank groups and its applications, Canad. J. Math., 72 (2020), 928-966.

[89] (With D. Wang), Shifted convolution sums of Fourier coefficients with squarefull kernel functions, Lith. Math. J., 60 (2020), 51-63.

[88] (With Y.J. Jiang), On an analogue of prime vectors among integer lattice points in ellipsoids for automorphic forms, Int. J. Number Theory, 16 (2020), no. 1, 145-160.

[87] Aperiodicity of signs of Hecke eigenvalues, Monatsh. Math., 191(2020), no. 1, 187-201.

[86] On pairwise maxima of powers of Hecke eigenvalues, Acta Arith., 192 (2020), no. 3, 249-257.

[85](With Y.J. Jiang), Quantitative non-vanishing results on L-functions, Qaurt. J. Math., 70 (2019), 813-830.

[84] (With Y.J. Jiang, Y.-K. Lau, E. Royer and J. Wu),On Fourier coefficients of modular forms of half integral weight at square-free integers, Math. Z., 293 (2019), 789-808.

[83] (With P. Xi), On triple correlations of Fourier coefficients of cusp forms. II, Int. J. Number Theory, 15 (2019), 713-722.

[82](With D. Wang), Averages of shifted convolutions of general divisor sums involving Hecke eigenvalues, J. Number Theory, 199(2019), 342-351.

[81](With Y.J. Jiang), Shifted convolution sums for higher rank groups, Forum Math., 31 (2019), 361-383.

[80](With M. Lou), Triple correlations of ternary divisor functions, J. Number Theory, 198 (2019), 318-345.

[79](With Y.J. Jiang), Exponential sums formed with the Möbius function, Indag. Math. (N.S.), 30(2019), 355-364.

[78](With Y.J. Jiang), On automorphic analogues of the Möbius randomness principle, J. Number Theory, 197(2019), 268-296.

[77] (With Z. Cui and J. Wu), The Selberg-Delange method in short intervals with some applications, Sci. China Math., 62(2019), 447-468.

[76] On sum of one prime, two squares of primes and powers of 2, Monatsh. Math., 187(2018), 113-123.

[75] Exponential sums with Fourier coefficients of automorphic forms, Math. Z., 289(2018), 267-278.

[74] (With P. Xi), On triple correlations of Fourier coefficients of cusp forms, J. Number Theory, 183(2018), 485-492.

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

[72] (With Y.J. Jiang), Exponential sums formed with the von Mangoldt function and Fourier coefficients of GL(m) automorphic forms, Monatsh. Math., 184(2017), 539-561.

[71] (With Y.J. Jiang), Fourth power moment of coefficients of automorphic L-functions for GL(m), Forum Math., 29(2017), 1199-1212.

[70](With Y.J. Jiang), On sums of Fourier coefficients of Maass cusp forms, Int. J. Number Theory, 13(2017), 1233-1243.

[69] (WithA. Sankaranarayanan), On the coefficients of triple product L-functions, Rocky Mountain J. Math., 47(2017), 553-570.

[68] (With Y.J. Jiang), Sums of coefficients of L-functions and applications, J. Number Theory, 171(2017), 56-70.

[67] Estimates for coefficients of certain L-functions, Monatsh. Math., 181(2016), 657-674.

[66] (With Y.J. Jiang and X. Yan), Mean value theorem connected with Fourier coefficients of Hecke-Maass forms for SL(m, Z), Math. Proc. Cambridge Philos. Soc., 161(2016), 339-356.

[65] (With F. Hou and Y.J. Jiang), On exponential sums involving coefficients of L-functions for SL(3,Z) over primes, Quart. J. Math., 67 (2016), no. 2, 285-301.

[64] (With J. Wu and W.G. Zhai), Shifted convolution of cusp-forms with θ -series, Ramanujan J., 40(2016), 115-133.

[63] (With F. Hou) Oscillations of Fourier coefficients of cusp forms over primes, J. Number Theory, 159(2016), 370-383.

[62] (With Y.J. Jiang) The average order of Hecke eigenvalues of Siegel cusp forms of genus 2, Ramanujan J., 38(2015), 465-480.

[61] (With W.J. Ma) On mean values of some arithmetic functions involving different number fields, Ramanujan J., 38(2015), 101-113.

[60] (With Y.J. Jiang), Average behavior of Fourier coefficients of Maass cusp forms for hyperbolic 3-manifolds, Monatsh. Math., 178(2015), 221-236.

[59] (With A. Sankaranarayanan) Higher moments of Fourier coefficients of cusp forms,

Canad. Math. Bull., 58(2015), 548-560.

[58] Shifted convolution sums of Fourier coefficients with divisor functions, Acta Math. Hungar., 146 (2015), 86-97.

[57](With H.C. Tang) Sums of Fourier coefficients related to Hecke eigencusp forms, Ramanujan J., 37(2015), 309-327.

[56] (With Y.J. Jiang) Uniform estimates for sums of coefficients of symmetric square L-function, J. Number Theory, 148(2015), 220-234.

[55] (With Y.J. Jiang) On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms, Acta Arith., 166(2014), 231-252.

[54] Sums of absolute values of cusp form coefficients and their application, J. Number Theory, 139(2014), 29-43.

[53] On averages of Fourier coefficients of Maass cusp forms, Arch. Math., 100(2013), 255-265.

[52] On higher moments of Fourier coefficients of holomorphic cusp forms II, Monatsh. Math., 169 (2013), 409-422.

[51](With H.W. Sun), The ternary Goldbach–Vinogradov theoremwith almost equal primes from the Beatty sequence, Ramanujan J., 30 (2013), 153-161.

[50] Mean values connected with the Dedekind zeta-function of a non-normal cubic field, Cent. Eur. J. Math., 11.2(2013), 274-282.

[49] (With J. Wu and W.G. Zhai) On a divisor problem related to the Epstein zeta-function III, Quart. J. Math., 63(2012), 953-963.

[48] (With J. Wu and W.G. Zhai) On a divisor problem related to the Epstein zeta-function IV, Acta Arith., 154(2012), 307-324.

[47] On general divisor problems involving Hecke eigenvalues, Acta Math. Hungar., 135(2012), 148-159.

[46] (With Y.-K. Lau and J. Wu), Integral power sums of Hecke eigenvalues, Acta Arith., 150(2011), 193-207.

[45] On higher moments of Fourier coefficients of holomorphic cusp forms, Canad. J. Math., 63(2011), 634-647.

[44] (With Z.X. Liu) Density of two squares and powers of 2, Int. J. Number Theory, 5(2011), 1317-1329.

[43] (With Y.-K. Lau) Sums of Fourier coefficients of cusp forms, Quart. J. Math., 62(2011), 687-716.

[42] On mean values of some arithmetic functions in number fields, Acta Math. Hungar., 132(2011), 348-357.

[41] (With Z.S. Yang), The average behavior of the coefficients of Dedekind zeta functions over square numbers, J. Number Theory, 131(2011), 1924-1938.

[40] (With Z.X. Liu) On unlike powers of prime and powers of 2, Acta Math. Hungar., 132(2011), 125-139.

[39] (With J. Wu and W.G. Zhai) On a divisor problem related to the Epstein zeta-function II, J. Number Theory, 131(2011), 1734-1742.

[38](With H.W. Sun) Primes in quadratic progressions on average, Acta Math. Sin. (Engl. Ser.), 27(2011), 1187-1194.

[37] (With Z.X. Liu), Two results on powers of a in Waring-Goldbach problem, J. Number Theory, 131(2011), 716-736.

[36] (With Z.X. Liu) Eight cubes of primes and powers of 2, Acta Arith., 145(2010),171-192.

[35] (With Y. H. Wang) Note on the number of integral ideals in Galois extensions, Sci. China Math., 53(2010), 2417-2424.

[34] (With H.G. Xia) Note on divisor function for quaternion algebras, J. Number theory, 130(2010), 2147-2156.

[33] On an open problem of Sankaranarayanan, Sci. China Math., 53(2010), 1319-1324.

[32] (With H.C. Tang) On some results of Hua in short intervals, Lith. Math. J., 50(2010), 54-70.

[31] On a divisor problem related to the Epstein zeta-function, Bull. London Math. Soc., 42(2010), 267-274.

[30] (With H.W. Sun) On fractional power moments of L-functions associated to certain cusp forms, Acta Appl. Math., 109(2010), 653-667.  

[29] Number of solutions of certain congruences, Acta Arith., 140(2009), 317-328.

[28] The sixth and eighth moments of Fourier coefficients of cusp forms, J. Number Theory, 129(2009), 2790-2880.  

[27] Uniform estimates for sums of Fourier coefficients of cusp forms, Acta Math. Hungar., 124(2009), 83-97.

[26] On sums involving coefficients of automorphic L-functions, Proc. Amer. Math. Soc.,, 137(2009), 2879-2887.  

[25] (With H.W. Sun) On a generalization of Hua's theorem with five squares primes, Acta Math. Hungar., 122(2009), 273-282.

[24] Average behavior of Fourier coefficients of cusp forms, Proc. Amer. Math. Soc., 137(2009), 1961-1969.

[23] The average value of Fourier coefficients of cusp forms in arithmetic progressions, J. Number Theory, 129(2009), 488-494.

[22] Additive functions on arithmetic progressions with large moduli, J. Number Theory, 129(2009), 477-487.

[21] (With W.G. Zhai) On the representation of large integers as sums of four almost equal squares of primes, Ramanujan J., 18(2009), 1-10.

[20] (With H.W. Sun) Integers represented as the sum of one prime, two squares of primes and powers of 2, Proc. Amer. Math. Soc., 137(2009), 1185-1191.

[19] (With X.M. Meng) On sums of a prime and four prime squares in short intervals, Acta Math.Sin. (Engl.Ser.), 24(2008), 1291-1302.

[18] On sums of a prime and four squares of primes in short intervals, J. Number theory, 128(2008), 805-819.  

[17] (With Y.F. Xu) Hua's theorem with nine almost equal prime variables, Acta Math. Hungar., 116(2007), 309-326.

[16] Gauss's three squares theorem with almost prime variables, Acta Arith., 128(2007), 391-399.

[15] (With H.X. Lao) On exponential sums over primes in short intervals, Monatsh. Math., 151(2007), 153-164.

[14] On Romanoff's constant and its generalized problem, Adv. Math. (China), 36(2007), 94-100.

[13] (With J.Y. Liu, T. Zhan) Exponential sums over primes in short intervals, Sci. China Ser. A, 49(2006), 611-619.

[12] Estimation of exponential sums over primes in short intervals, Acta Math. Sin., 49 (2006), 693-698.

[11] Hua's Theorem on five almost equal prime squares, Acta Math. Sin. (Engl. Ser.), 22(2006), 907-916.  

[10] Note on a result of Hua, Adv. Math. (China), 35(2006), 343-349.  

[9] Sums of nine almost equal prime cubes, Acta Math. Sin., 49(2006), 195-204.  

[8] Hua's Theorem with five almost equal prime variables, Chinese Ann. Math. Ser. B, 26(2005), 291-304.  

[7] (With W.G. Zhai) On three-dimensional divisor problem of (a,a,b) type, Adv. Math. (China), 33(2004), 195-202.  

[6] (With J.Y. Liu) Four squares of primes and 165 powers of 2, Acta Arith., 114(2004), 55-70.

[5] (With W.G. Zhai) The divisor problem on the Beatty sequence, Acta Math. Sin., 47(2004), 1213-1216.

[4] (With W.G. Zhai) On the sum of multi-dimensional divisor function on special sequence, Adv. Math. (China), 32(2003), 660-664.

[3] On sums of two squares of primes and a cube of a prime, Northeast. Math. J., 19(2003), 99-102.

[2] (With W.G. Zhai) A special two-dimensional divisor problem, Chinese Pure and Applied Mathematics, 18(2002), 348-352.

[1] (With W.G. Zhai) A special divisor problem, Acta Math. Sin., 45(2002), 991-1004.

Scientific research projects：

[11] 2021-2026：Member of the National Key Research and Development Program of China (No. 2021YFA1000700), by Ministry of Science and Technology of the People's Republic of China .

[10] 2021-2025: Member of the Key Project of National Natural Foundation (Grant No.12031008), by the National Natural Science Foundation.

[9] 2018-2021: National Natural Foundation (Grant No. 11771252), by the National Natural Science Foundation.

[8] 2016-2020: Member of the Key Project of National Natural Foundation (Grant No. 11531008 ), by the National Natural Science Foundation.

[7] 2012-2015: National Natural Foundation (Grant No. 11171182), by the National Natural Science Foundation.

[6] 2011-2014: Shandong Province Natural Science Foundation for distinguished Young Scholars (Grant No. JQ201102), by Shandong Province Natural Science Foundation.

[5] 2010-2012: Program for New Century Excellent Talents in University (Grant No. NCET-10-0548), by the Ministry of Education of the People's Republic of China.  

[4] 2011-2014: Member of the Key Project of National Natural Foundation (Grant No.11031004), by the National Natural Science Foundation.

[3] 2009-2011: Shandong Province Natural Science Foundation (Grant No. ZR2009AM007), by Shandong

[2] 2008-2010: National Natural Foundation (Grant No. 10701048), by the National Natural Science Foundation.

[1] 2006-2007: Tianyuan Mathematics Foundation (Grant No. 10526028), by the National Natural Science Foundation.