Curriculum Vitae

Name

Lv Guangshi    

Contact Information   

School of Mathematics & SDU-ANU JSC

Shandong University

Shandong 250100 

P. R. China 

Email: gslv(at)sdu.edu.cn

Education    

Ph.D.: Shandong University, 2004

M.S.:  Shandong Normal University, 2001 

B.S.:  Shandong Normal University, 1998

Employment 

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

2004.08-2006.09: Assistant Professor, Shandong University

Research Interests  

Number Theory, Additive number theory, automorphic forms, L-function, exponential sums

Awards

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

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

Grants

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

2018-2021: National Natural Foundation (Grant No. 11771252), 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.

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

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

2010-2012: Program for New Century Excellent Talents in University (Grant No. NCET-10-0548), by the Ministry of Education. 

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

2010-2012: Independent Innovation Foundation of Shandong University, by Shandong University.

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

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

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

2005-2007: Young Scholars Foundation, by School of Mathematics, Shandong University.

Publications 

[98] (With Y. Jiang, J. Thorner, Z. Wang), A Bombieri-Vinogradov theorem for higher-rank groups, Int. Math. Res. Not. IMRN, (2021), 1-54 (online).

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

[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.W. Wang), Exponential sums with multiplicative coefficients without the Ramanujan conjecture, Math. Ann., 379 (2020), 589–632.

[94] (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.

[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), no. 3-4, 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), no. 4, 928–966.

[89] (With D. Wang), Shifted convolution sums of Fourier coefficients with squarefull kernel functions, Lith. Math. J., 60 (2020), no. 1, 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, Q. 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, Q. J. Math., 67 (2016), no. 2, 285–301.

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

[63] (With Y.J. Jiang), Average behavior of Fourier coefficients of Maass cusp forms for hyperbolic 3-manifolds, Monatshfte fur Mathematik, 178(2015), 221-236.

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

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

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

Canadian Mathematical Bulletin, 58(2015), 548-560.

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

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

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

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

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

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

[53] On averages of Fourier coefficients of Maass cusp forms, Archiv der Mathematik, 100(2013), 255–265. 

[52] Mean values connected with the Dedekind zeta-function of a non-normal cubic field, Central European Journal of Mathematics, 11.2(2013), 274-282.

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

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

[49] (With J. Wu and W.G. Zhai) On a divisor problem related to the Epstein zeta-function IV, Acta Arith., 154.3(2012), 307-324.

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

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

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

[43] On mean values of some arithmetic functions in number fields, Acta Math. Hungar., 132(2011), 1924-1938.

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

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

[40] (With J. Wu and W.G. Zhai) On a divisor problem related to the Epstein zeta-function II,

Journal of Number Theory, 131(2011), 1734-1742.

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

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

[37] On higher moments of Fourier coefficients of holomorphic cusp forms, Canadian Journal of Mathematics, 63(2011), 634-647.

[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, Science China: Mathematics, 53(2010), 2417-2424.

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

[33] On a divisor problem related to the Epstein zeta-function, Bulletin of the London Mathematical Society, 42(2010), 267-274.

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

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

[30] Number of solutions of certain congruences, Acta Arith., 140.4(2009), 317-328.

[29] The sixth and eighth moments of Fourier coefficients of cusp forms, Journal of Number Theory, 129.11(2009), 2790-2880. 

[28] On an open problem of Sankaranarayanan, Science in China Series A: Mathematics, 39.8(2009), 1023-1028.

[27] Uniform estimates for sums of Fourier coefficients of cusp forms, Acta Math. Hungar., 124.1-2(2009),83-97.

[26] On sums involving coefficients of automorphic L-functions, Proceedings of the AMS, 137.9(2009), 2879-2887. 

[25] Average behavior of Fourier coefficients of cusp forms, Proceedings of the AMS, 137.6(2009), 1961-1969.

[24] (With H.W. Sun) On a generalization of Hua's theorem with five squares primes, Acta Math. Hungar., 122.3(2009), 273-282.

[23] (With W.G. Zhai) On the representation of large integers as sums of four almost

equal squares of primes, The Ramanujan Journal, 18(2009), 1-10.

[22] (With H.W. Sun) Integers represented as the sum of one prime, two squares of primes and powers of 2, Proceedings of the AMS, 137.4(2009), 1185-1191.

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

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

[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, Journal of 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, Monatshfte fur Mathematik, 151(2007), 153-164.

[14] On Romanoff's Constant and Its Generalized Problem, Chinese Advance in Mathematics, 36(2007), 94-100.

[13] (With J.Y. Liu, T. Zhan) Exponential sums over primes in short intervals, Sci. China Ser. A, 49(2006), 449-457.

[12] On the 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, Chinese Advances in Mathematics, 35(2006), 343-348. 

[9] On 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, Chinese Advances in Mathematics, 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, Chinese Advances in Mathematics, 32(2003), 660-664.

[3] On sums of two squares of primes and a cube of a prime, Northeastern Mathematics Journal, 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.