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Liu, Zhiguo ( 刘治国 ) 
Title: Professor
Department: Pure Mathematics
Office: Room 336, Math Building
Telephone: 54342646-336
Email: zgliu@math.ecnu.edu.cn
Homepage: http://math.ecnu.edu.cn/~zgliu
Homepage2: https://faculty.ecnu.edu.cn/_s42/lzg/main.psp
Research Interest
Theta functions, q-series, Number Theory, Ramanujan's Notebooks
Resume
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1983年7月毕业于新乡师范学院数学系获学士学位
1983年7月-1984年8月任高中数学教师
1985年9月-2003年4月在新乡市教育学院任教
1998年元月-1999年元月在英国Sussex大学访问
2001年6月-2003年4月在新加坡国立大学访问
2003年起在华东师范大学任教

1998年获王宽城英国皇家学会研究奖学金
1998年获新乡市第三届“青年楷模”称号
1999年获曾宪梓优秀教师二等奖
2001年获新乡市劳动模范称号
2002年入选《新乡五千年》名人录

Selected Publications
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[1] Parameter augmentation for basic hypergeometric series. I. Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), 111--129, Progr. Math., 161, Birkh?user Boston, Boston, MA, 1998. (with Chen, William Y. C.)
[2] Parameter augmentation for basic hypergeometric series. II. Journal of Combinatorics Theory Series A, 80 (1997), 175--195. (with Chen, William Y. C.)
[3] Residue theorem and theta function identities, Ramanujan Journal, 5 (2001), 129--151.
[4] On the representation of integers as sums of squares, q-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), 163--176, Contemp. Math., 291, Amer. Math. Soc., Providence, RI, 2001.
[5] Incomplete Elliptic Integral Analogues of Jacobi's inversion formula for the incomplete elliptic integral of the first kind, Advances in Mathematics, 174 (2003), 69-88.(with H. H . Chan)
[6] An Expansion Formula for q-Series and Applications, The Ramanujan Journal, 6 (2002), 429-447.
[7] Some Eisenstein Series Identities Related To Modular Equations of the Seventh Order, Pacific Mathematics Journal, 209 (2003), 103-130.
[8] Domb's numbers and Ramanujan-Sato type series for ( with Heng Huat Chan, Song Heng Chan ), Advances in Mathematics. 186 (2004), 396-410.
[9] A theta function identity and its implications, Trans. of the Amer. Math. Soc. 357 (2005), 825-835
[10] A three term theta function identity and its applications, Advances in Mathematics. 195(2005), 1-23

Recent Publications(From MathSciNet)
MR5043772 Pending Mehmood, Ahsan; Liu, Zhi-Guo; Younis, Muhammad; Samraiz, Muhammad; Budak, Hüseyin; Khan, Bilal Visualization of fractional reverse inequalities involving interval-valued convexity and their application. J. Comput. Appl. Math. 485 (2026), Paper No. 117582, 19 pp. 26D15 (26A33 26A51)
Publication Year 2026 Indexed 2026-05-04
MR5015310 Indexed Mehmood, Ahsan; Liu, Zhi-Guo; Samraiz, Muhammad; Usta, Fuat; Arjika, Sama Numerical investigation of a human liver model based on generalized fractional operators and neural networks. Math. Comput. Model. Dyn. Syst. 32 (2026), no. 1, Paper No. 2610965, 29 pp. 92B05 (34A08)
Publication Year 2026 Indexed 2026-03-18
MR4941983 Reviewed Younis, Muhammad; Liu, Zhi Guo; Samraiz, Muhammad; Mehmood, Ahsan A new formulation of Hermite-Hadamard-Fejer inequalities connected with an extended fractional operator. J. Inequal. Appl. 2025, Paper No. 92, 21 pp. 26D15 (26A33 26A51)
Publication Year 2025 Indexed 2025-09-29 Review Published2025-10-09
MR4905641 Indexed Mehmood, Ahsan; Liu, Zhi-Guo; Samraiz, Muhammad; Usta, Fuat; Arjika, Sama Innovative techniques to chaotic dynamics and kinetic differ-integral equations. Math. Comput. Model. Dyn. Syst. 31 (2025), no. 1, Paper No. 2490515, 23 pp. 34A08 (34C28)
Publication Year 2025 Indexed 2025-07-10
MR4886621 Reviewed Chan, Heng Huat; Liu, Zhi-Guo Ramanujan's theory of elliptic functions to the cubic base. Results Math. 80 (2025), no. 3, Paper No. 81, 20 pp. (Reviewer: Abd Raouf Chouikha) 33E05 (11F27 33C05)
Publication Year 2025 Indexed 2025-05-16 Review Published2025-07-24
MR4868791 Reviewed Chen, Dandan; Liu, Zhiguo New proofs of theorems on $q$-orthogonal functions. Int. J. Number Theory 21 (2025), no. 2, 473–486. 33D15 (05A30 33D45 42C05)
Publication Year 2025 Indexed 2025-04-14 Review Published2025-04-29
MR4848496 Reviewed Chan, Heng Huat; Chan, Song Heng; Liu, Zhi-Guo Elementary derivations of the Rogers-Fine identity and other $q$-series identities. Discrete Math. 348 (2025), no. 5, Paper No. 114387, 14 pp. (Reviewer: David M. Bressoud) 11P81 (05A19 05A30)
Publication Year 2025 Indexed 2025-03-18 Review Published2025-06-25
MR4843375 Reviewed Liu, Zhi-Guo On a transformation of triple $q$-series and Rogers-Hecke type series. SIGMA Symmetry Integrability Geom. Methods Appl. 20 (2024), Paper No. 086, 37 pp. (Reviewer: Jian Cao) 05A30 (11E25 32A05 32A10 33D05 33D15)
Publication Year 2024 Indexed 2025-02-26 Review Published2025-05-07
MR4675090 Reviewed Liu, Zhi Guo A multiple $q$-translation formula and its implications. Acta Math. Sin. (Engl. Ser.) 39 (2023), no. 12, 2338–2363. 05A30 (32A05 33D05 33D15 33D45)
Publication Year 2023 Indexed 2024-01-22 Review Published2024-11-12
MR4664498 Reviewed Liu, Zhiguo A multiple $q$-exponential differential operational identity. Acta Math. Sci. Ser. B (Engl. Ed.) 43 (2023), no. 6, 2449–2470. 33D15 (05A30 32D15)
Publication Year 2023 Indexed 2023-12-12 Review Published2024-08-13
MR4596046 Reviewed Liu, Zhiguo A $q$-operational equation and the Rogers-Szegő polynomials. Sci. China Math. 66 (2023), no. 6, 1199–1216. (Reviewer: Gaurav Bhatnagar) 33D15 (05A30 05A40)
Publication Year 2023 Indexed 2023-06-30 Review Published2024-02-29
MR4584520 Reviewed Liu, Zhi-Guo The Kronecker theta function and a decomposition theorem for theta functions I. Ramanujan J. 61 (2023), no. 1, 149–173. 33D15 (11F27 11F37)
Publication Year 2023 Indexed 2023-07-07 Review Published2024-02-23
MR4399005 Reviewed Khan, Bilal; Liu, Zhi-Guo; Shaba, Timilehin Gideon; Araci, Serkan; Khan, Nazar; Khan, Muhammad Ghaffar Applications of $q$-derivative operator to the subclass of bi-univalent functions involving $q$-Chebyshev polynomials. J. Math. 2022, Art. ID 8162182, 7 pp. 30C45 (33C45)
Publication Year 2022 Indexed 2022-05-05 Review Published2022-05-12
MR4382182 Reviewed Liu, Zhi-Guo; Zhou, Nian Hong Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions. Ramanujan J. 57 (2022), no. 3, 1085–1123. (Reviewer: Dazhao Tang) 11F27 (05A17 11F30 11P82)
Publication Year 2022 Indexed 2022-04-21 Review Published2022-08-25
MR4322453 Reviewed Khan, Bilal; Liu, Zhi-Guo; Srivastava, H. M.; Araci, Serkan; Khan, Nazar; Ahmad, Qazi Zahoor Higher-order $q$-derivatives and their applications to subclasses of multivalent Janowski type $q$-starlike functions. Adv. Difference Equ. 2021, Paper No. 440, 15 pp. 30C45 (05A30 11B65 30C50)
Publication Year 2021 Indexed 2021-11-16 Review Published2021-12-10
MR4310091 Reviewed Liu, Zhi-Guo On the Askey-Wilson polynomials and a $q$-beta integral. Proc. Amer. Math. Soc. 149 (2021), no. 11, 4639–4648. (Reviewer: Jiang Zeng) 33D15 (05A30 33D45)
Publication Year 2021 Indexed 2021-11-08 Review Published2022-02-22
MR4298492 Reviewed Liu, Zhi-Guo A universal identity for theta functions of degree eight and applications. Hardy-Ramanujan J. 43 (2020), 129–172. 33E05 (11F11 11F20 11F27)
Publication Year 2020 Indexed 2021-10-07 Review Published2022-06-01
MR4237815 Reviewed Liu, Zhi-Guo On the complex Hermite polynomials. Filomat 34 (2020), no. 2, 409–420. 33C45 (32A05 35C11)
Publication Year 2020 Indexed 2021-07-06 Review Published2021-07-14
MR3951416 Reviewed Liu, Zhi-Guo Askey-Wilson polynomials and a double $q$-series transformation formula with twelve parameters. Proc. Amer. Math. Soc. 147 (2019), no. 6, 2349–2363. (Reviewer: David M. Bressoud) 33D45 (05A30 11E25 33D15)
Publication Year 2019 Indexed 2019-07-11 Review Published2019-10-30
MR3827149 Reviewed Cao, Jian; Srivastava, H. M.; Liu, Zhi-Guo Some iterated fractional $q$-integrals and their applications. Fract. Calc. Appl. Anal. 21 (2018), no. 3, 672–695. 05A15 (11B65 26A33 33D15 33D45 33D60 39A13)
Publication Year 2018 Indexed 2018-09-14 Review Published2018-10-08

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