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Guangshi Lü

Email: gslv@sdu.edu.cn

Address: School of Mathematics

Shandong University

Jinan, Shandong 250100

Personal Homepage

Research Interests:

Additive number theory, automorphic forms, L-function and exponential sums.


Publications

[112] (with S. Luo) Maximum values of multiplicative functions on short intervals, Acta Arith. 215 (2024), no.3, 229–247.

[111] (with F.Hou) Triple correlation sums of coefficients of Maass forms for SL4(ℤ), Q. J. Math. 75 (2024), no.3, 1123–1148.

[110] (with F.Hou) An explicit Voronoǐformula for SL3(ℝ) newforms underlying the symmetric lifts in the level aspect, Int. J. Number Theory 20 (2024), no.3, 797–809.

[109] (with Q. Ma) Exponential sums with the Dirichlet coefficients of Rankin-Selberg L-functions, Monatsh. Math. 204 (2024), no.1, 127–155.

[108] (with Y. Jiang) Correlations of multiplicative functions with coefficients of automorphic L-functions, Int. Math. Res. Not. IMRN2024, no.2, 1733–1770.

[107] (with Q. Ma) Monotone chains in modulus of two classes of Dirichlet coefficients, Acta Math. Sin. (Engl. Ser.) 39 (2023), no.6, 1101–1114.

[106] (with Y. Jiang) A survey on coefficients of automorphic L-functions, Adv. Math. (China) 52 (2023), no. 2, 201–223.

[105] (with Y. Jiang, J. Thorner, Z. Wang) A Bombieri-Vinogradov theorem for higher-rank groups

Jiang, Yujiao; Lü, Guangshi; Thorner, Jesse; Wang, Zihao. Int. Math. Res. Not. IMRN2023, no.1, 482–535.

[104] (with Y. Jiang, Z. Wang) Möbius randomness law for GL(m) automorphic L-functions twisted by additive characters, Proc. Amer. Math. Soc. 151 (2023), no. 2, 475–488.

[103] (with G. Hu) Jutila's circle method and GL(2)×GL(2) shifted convolution sums, J. Number Theory 242 (2023), 709–724.

[102] (with Y. Jiang, Z. Wang) Averaged forms of two conjectures of Erdős and Pomerance, and their applications, Adv. Math. 409 (2022), Paper No. 108592, 42 pp.

[101] (with G. Hu) Shifted convolution sums of GL(m) cusp forms with Θ-series, Ramanujan J. 56 (2021), no. 2, 555–584.

[100] (with Y. Jiang) The generalized Bourgain-Sarnak-Ziegler criterion and its application to additively twisted sums on GLm, Sci. China Math. 64 (2021), no. 10, 2207–2230.

[99] (with Y. Jiang) Cancellation in algebraic twisted sums on GLm, Forum Math. 33 (2021), no.4, 1061–1082.

[98] (with Y. Jiang, Z. Wang) A Bombieri-Vinogradov theorem for number fields, Mathematika 67 (2021), no.3, 678–713.

[97] (with Y. Jiang, Z. Wang) Exponential sums with multiplicative coefficients without the Ramanujan conjecture, Math. Ann. 379 (2021), no. 1-2, 589–632.

[96] (with G. Hu) Sums of higher divisor functions, J. Number Theory 220 (2021), 61–74.

[95] (with G. Hu) Shifted convolution sums for SL(m), Manuscripta Math. 163 (2020), no. 3-4, 375–394.

[94] (with G. Hu, Y. Jiang) The Fourier coefficients of Θ-series in arithmetic progressions, Mathematika 66 (2020), no. 1, 39–55.

[93] (with Y. Jiang) The Bombieri-Vinogradov theorem on higher rank groups and its applications,Canad. J. Math. 72 (2020), no.4, 928–966.

[92] (with D. Wang) Shifted convolution sums of Fourier coefficients with squarefull kernel functions, Lith. Math. J. 60 (2020), no. 1, 51–63.

[91] (with Y. 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.

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

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

[88] (with Y. Jiang) Quantitative non-vanishing results on L-functions, Q. J. Math. 70 (2019), no.3, 813–830.

[87] (with Y. Jiang, Y-K. Lau, E. Royer, J. Wu) On Fourier coefficients of modular forms of half integral weight at squarefree integers,Math. Z. 293 (2019), no. 1-2, 789–808.

[86] (with P. Xi) On triple correlations of Fourier coefficients of cusp forms. II, Int. J. Number Theory 15 (2019), no.4, 713–722.

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

[84] (with Y. Jiang) Shifted convolution sums for higher rank groups,Forum Math. 31 (2019), no.2, 361–383.

[83] (with M. Lou) Triple correlations of ternary divisor functions, J. Number Theory 198 (2019), 318–345.

[82] (with Y. Jiang) Exponential sums formed with the Möbius function,Indag. Math. (N.S.) 30 (2019), no. 2, 355–364.

[81] (with Y. Jiang) On automorphic analogues of the Möbius randomness principle, J. Number Theory 197 (2019), 268–296.

[80] (with Z. Cui, J. Wu) The Selberg-Delange method in short intervals with some applications, Sci. China Math. 62 (2019), no. 3, 447–468.

[79] On sum of one prime, two squares of primes and powers of 2,Monatsh. Math. 187 (2018), no.1, 113–123.

[78] Exponential sums with Fourier coefficients of automorphic forms, Math. Z. 289 (2018), no. 1-2, 267–278.

[77] (with P. Xi) On triple correlations of Fourier coefficients of cusp forms J. Number Theory 183 (2018), 485–492.

[76] (with Y. Jiang) Oscillations of Fourier coefficients of GL(m) Hecke-Maass forms and nonlinear exponential functions at primes, Funct. Approx. Comment. Math. 57 (2017), no. 2, 185–204.

[75] (with Y. Jiang) Exponential sums formed with the von Mangoldt function and Fourier coefficients of GL(m) automorphic forms,Monatsh. Math. 184 (2017), no. 4, 539–561.

[74] (with Y. Jiang) Fourth power moment of coefficients of automorphic L-functions for GL(m),Forum Math. 29 (2017), no. 5, 1199–1212.

[73] (with Y. Jiang) On sums of Fourier coefficients of Maass cusp forms, Int. J. Number Theory 13 (2017), no.5, 1233–1243.

[72] (with S. Ayyadurai) On the coefficients of triple product L-functions,Rocky Mountain J. Math. 47 (2017), no. 2, 553–570.

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

[70]Estimates for coefficients of certain L-functions. Monatsh. Math. 181 (2016), no. 3, 657–674.

[69] (with Y. Jiang, X. Yan) Mean value theorem connected with Fourier coefficients of Hecke-Maass forms for SL(m,ℤ), Math. Proc. Cambridge Philos. Soc. 161 (2016), no. 2, 339–356.

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

[67] (with J. Wu, W. Zhai) Shifted convolution of cusp-forms with θ-series, Ramanujan J. 40 (2016), no. 1, 115–133.

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

[65] (with Y. Jiang) The average order of Hecke eigenvalues of Siegel cusp forms of genus 2, Ramanujan J. 38 (2015), no. 3, 465–480.

[64] (with J. Ma) On mean values of some arithmetic functions involving different number fields,Ramanujan J. 38 (2015), no. 1, 101–113.

[63] (with Y. Jiang) Average behavior of Fourier coefficients of Maass cusp forms for hyperbolic 3-manifolds, Monatsh. Math. 178 (2015), no. 2, 221–236.

[62] (with S. Ayyadurai) Higher moments of Fourier coefficients of cusp forms, Canad. Math. Bull. 58 (2015), no. 3, 548–560.

[61] Shifted convolution sums of Fourier coefficients with divisor functions,Acta Math. Hungar. 146 (2015), no. 1, 86–97.

[60] (with H. Tang) Sums of Fourier coefficients related to Hecke eigencusp forms, Ramanujan J. 37 (2015), no. 2, 309–327.

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

[58] (with Y. Jiang) On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms, Acta Arith. 166 (2014), no. 3, 231–252.

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

[56] On Fourier coefficients of automorphic forms,Ser. Number Theory Appl, 8, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013, 182–200. ISBN: 978-981-4452-44-1

[55] On averages of Fourier coefficients of Maass cusp forms,Arch. Math. (Basel) 100 (2013), no.3, 255–265.

[54] On higher moments of Fourier coefficients of holomorphic cusp forms II, Monatsh. Math. 169 (2013), no. 3-4, 409–422.

[53] (with H. Sun) The ternary Goldbach-Vinogradov theorem with almost equal primes from the Beatty sequence,Ramanujan J. 30 (2013), no. 2, 153–161.

[52] Mean values connected with the Dedekind zeta-function of a non-normal cubic field, Cent. Eur. J. Math. 11 (2013), no. 2, 274–282.

[51] (with J. Wu, W. Zhai) On a divisor problem related to the Epstein zeta-function,  III, Q. J. Math. 63 (2012), no. 4, 953–963.

[50] (with J. Wu, W. Zhai) On a divisor problem related to the Epstein zeta-function, IV, Acta Arith. 154 (2012), no. 3, 307–324.

[49] On general divisor problems involving Hecke eigenvalues, Acta Math. Hungar. 135 (2012), no. 1-2, 148–159.

[48] (with Y-K. Lau, J. Wu) Integral power sums of Hecke eigenvalues, Acta Arith. 150 (2011), no. 2, 193–207.

[47] On higher moments of Fourier coefficients of holomorphic cusp forms, Canad. J. Math. 63 (2011),  no. 3, 634–647.

[46] (with Z. Liu) Density of two squares of primes and powers of 2, Int. J. Number Theory 7 (2011), no. 5, 1317–1329.

[45] (with Y-K. Lau) Sums of Fourier coefficients of cusp forms, Q. J. Math. 62 (2011), no. 3, 687–716.

[44] On mean values of some arithmetic functions in number fields, Acta Math. Hungar. 132 (2011), no. 4, 348–357.

[43] (with Z. Yang) The average behavior of the coefficients of Dedekind zeta function over square numbers, J. Number Theory 131 (2011), no.10, 1924–1938.

[42] (with Z. Liu) On unlike powers of primes and powers of 2,Acta Math. Hungar. 132 (2011), no.1-2, 125–139.

[41] (with J. Wu, W. Zhai) On a divisor problem related to the Epstein zeta-function, II, J. Number Theory 131 (2011), no. 9, 1734–1742.

[40] (with H. Sun) Prime in quadratic progressions on average, Acta Math. Sin. (Engl. Ser.) 27 (2011), no. 6, 1187–1194.

[39] (with Z. Liu) Two results on powers of 2 in Waring-Goldbach problem, J. Number Theory 131 (2011), no. 4, 716–736.

[38] (with Z. Liu) Eight cubes of primes and powers of 2, Acta Arith. 145 (2010), no. 2, 171–192.

[37] (with Y. Wang)N ote on the number of integral ideals in Galois extensions, Sci. China Math. 53 (2010), no. 9, 2417–2424.

[36] (with H. Xia) Note on divisor function for quaternion algebras, J. Number Theory 130 (2010), no. 10, 2147–2156.

[35] On an open problem of Sankaranarayanan, Sci. China Math. 53 (2010), no.5, 1319–1324.

[34] (with H. Tang) On some results of Hua in short intervals, Lith. Math. J. 50 (2010), no. 1, 54–70.

[33] On a divisor problem related to the Epstein zeta-function, Bull. Lond. Math. Soc. 42 (2010), no. 2, 267–274.

[32] (with H. Sun) Erratum: On fractional power moments of L-functions associated with certain cusp forms, Acta Appl. Math. 109 (2010), no. 2, 669–670.

[31] (with H. Sun) On fractional power moments of L-functions associated with certain cusp forms, Acta Appl. Math. 109 (2010), no. 2, 653–667.

[30] Number of solutions of certain congruences, Acta Arith. 140 (2009), no. 4, 317–328.

[29] The sixth and eighth moments of Fourier coefficients of cusp forms, J. Number Theory 129 (2009), no. 11, 2790–2800.

[28] Uniform estimates for sums of Fourier coefficients of cusp forms, Acta Math. Hungar. 124 (2009), no. 1-2, 83–97.

[27] On sums involving coefficients of automorphic L-functions,Proc. Amer. Math. Soc. 137 (2009), no. 9, 2879–2887.

[26] (with H.Sun) On a generalization of Hua's theorem with five squares of primes, Acta Math. Hungar. 122 (2009), no. 3, 273–282.

[25] Average behavior of Fourier coefficients of cusp forms, Proc. Amer. Math. Soc. 137 (2009), no. 6, 1961–1969.

[24] The average value of Fourier coefficients of cusp forms in arithmetic progressions, J. Number Theory 129 (2009), no. 2, 488–494.

[23] Additive functions on arithmetic progressions with large moduli, J. Number Theory 129 (2009), no. 2, 477–487.

[22] (with W. Zhai) On the representation of large integers as sums of four almost equal squares of primes,Ramanujan J. 18 (2009), no.1, 1–10.

[21] (with H. Sun) Integers represented as the sum of one prime, two squares of primes and powers of 2, Proc. Amer. Math. Soc. 137 (2009), no. 4, 1185–1191.

[20] (with Y. Xu) Sums of a prime and the squares of three primes in short intervals, Pure Appl. Math. (Xi'an) 24 (2008), no. 1, 190–199.

[19] (with X. Meng) On sums of a prime and four prime squares in short intervals, Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 8, 1291–1302.

[18] On sums of a prime and four prime squares in short intervals, J. Number Theory 128 (2008), no. 4, 805–819.

[17] On Romanoff's constant and its generalized problem, Adv. Math. (China) 36 (2007), no. 1, 94–100.

[16]  (with Y. Xu) Hua's theorem with nine almost equal prime variables,Acta Math. Hungar. 116 (2007), no. 4, 309–326.

[15] (with H. Lao) On exponential sums over primes in short intervals, Monatsh. Math. 151 (2007), no. 2, 153–164.

[14] Gauss's three squares theorem with almost prime variables, Acta Arith. 128 (2007), no. 4, 391–399.

[13] Note on a result of Hua, Adv. Math. (China) 35 (2006), no. 3, 343–349.

[12] Estimation of exponential sums over primes in short intervals, Acta Math. Sinica (Chinese Ser.) 49 (2006), no. 3, 693–698.

[11] (with J. Liu, T. Zhan) Exponential sums over primes in short intervals, Sci. China Ser. A 49 (2006), no. 5, 611–619.

[10] Sums of nine almost equal prime cubes, Acta Math. Sinica (Chinese Ser.) 49 (2006), no. 1, 195–204.

[9] Hua's theorem on five almost equal prime squares, Acta Math. Sin. (Engl. Ser.) 22 (2006), no.3, 907–916.

[8] Hua's theorem with five almost equal prime variables, Chinese Ann. Math. Ser. B 26 (2005), no. 2, 291–304.

[7] (withW. Zhai) The divisor problem for the Beatty sequences, Acta Math. Sinica (Chinese Ser.) 47 (2004), no. 6, 1213–1216.

[6] (withW. Zhai) On three-dimensional divisor problem of (a,a,b) type, Adv. Math. (China) 33 (2004), no. 2, 195–202.

[5] (with J. Liu) Four squares of primes and 165 powers of 2, Acta Arith. 114 (2004), no. 1, 55–70.

[4] (with W. Zhai) The sum of multidimensional divisor functions on a special sequence, Adv. Math. (China) 32 (2003), no. 6, 660–664.

[3] On sums of two squares of primes and a cube of a prime, Northeast. Math. J. 19 (2003), no. 2, 99–102.

[2] (with W. Zhai) A special two-dimensional divisor problem, Pure Appl. Math. (Xi'an) 18 (2002), no. 4, 348–352.

[1] (with W. Zhai) A special divisor problem,Acta Math. Sinica (Chinese Ser.) 45 (2002), no. 5, 991–1004.