Research Areas: Number Theory

  gslv@sdu.edu.cn

PhD: 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

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

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

[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.

[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 Province Natural Science Foundation.

[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.