Research Interest

• • Harmonic Analysis in Finite Fields

  • Fourier analysis

  • Analytic Number Theory

  • Geometric Combinatorics

• • Google Scholar

  • Arxiv

  • Mathscinet

61.  Mean value theorems for rational exponential sums , (joint work with Igor  Shparlinski),  Finite Fields Appl.  accepted for publication (2025).

60.  Connections between S-operators and restriction estimates for spheres over finite fields, (joint work with Hunseok Kang),  J. Math. Anal. Appl. 554 (2026),  Paper No. 129936, 22 pp. 

59.  Multi-linear forms, graphs and L^p-improving measures in  F_q^d, (joint work with Pablo Bhowmik, Alex Iosevich, and Thang Pham),   Canad. J. Math. 77 (2025), no. 1, 208–251.  

58.  A spherical extension theorem and applications in positive characteristic,   (joint work with  Thang Pham),  Finite Fields Appl. 101 (2025), Paper No. 102515, 20 pp.

57.  The quotient set of the quadratic distance set over finite fields, (joint work with Alex Iosevich and Firdavs Rakhmonov), Forum Math.   36 (2024), no. 5, 1341–1358. 

56.  Falconer type functions in three variables (joint work with Thang Pham and Chun-Yen Shen),   J. Funct. Anal.  286 (2024) ,  no. 4, Paper No.  110246.

55.  Structural theorems on the distance sets over finite fields, (joint work with Minh Quy Pham and Thang Pham),  Forum Math.  35 (2023), no. 4, 925-938.

54. Mattila-Sjolin type functions: A finite field model, (joint work with Daewoong Cheong, Thang Pham and Chun-Yen Shen), Vietnam J. Math. 51 (2023),  no. 2, 421-434. 

53. Configurations of rectangles in F_q^2, (joint work with Sujin Lee, Thang Pham, and Chun-Yen Shen), Finite Fields Appl. 86 (2023), Paper No. 102147, 13 pp.

52. Restriction estimates for the flat disks over finite fields, J. Math. Anal. Appl. 518 (2023), no. 2, Paper No. 126714, 21 pp. 

51. On the finite field cone restriction conjecture in four dimensions and applications in incidence geometry, (joint work with Sujin Lee and Thang Pham), Int. Math. Res. Not. IMRN (2022), no. 21, 17079-17111. 

50. On the Mattila-Sjolin distance theorem for product sets, (joint work with Thang Pham and Chun-Yen Shen), Mathematika 68 (2022), no. 4, 1258 -1267. 

49. Note on the pinned distance problem over finite fields. J. Chungcheong Math. Soc. 35 (2022), no. 3, 227-234. 

48. A point-sphere incidence bound in odd dimensions and applications (joint work with Thang Pham), C. R. Math. Acad. Sci. Paris 360 (2022), 687 -698. 

47. Averages and maximal averages over Product j-varieties in finite fields (joint work with Sujin Lee), Finite Fields Appl. 79 (2022), Paper No. 101984, 13 pp. 

46. Extension theorems for Hamming varieties over finite fields, (joint work with Daewoong Cheong, and Thang Pham), Proc. Amer. Math. Soc. 150 (2022), no. 1, 161-170. 

45. An asymmetric bound for sum of distance sets, (joint work with Daewoong Cheong and Thang Pham), (Russian) English version published in Proc. Steklov Inst. Math. 314 (2021), no. 1, 279-289. Tr. Mat. Inst. Steklova 314 (2021),  290-300. 

44. On restriction estimates for the zero radius sphere over finite fields, (joint work with Alex Iosevich, Sujin Lee, Thang Pham, and Chun-Yen Shen), Canad. J. Math. 73 (2021) no. 3, 769-786. 

43. Extension theorems and a connection to the Erdos-Falconer distance problem over finite fields, (joint work with Thang Pham, and Le Anh Vinh), J. Funct. Anal. 281 (2021), no. 8, 109137, 54 pp. 

42. Distribution of the determinants of sums of matrices, (joint work with Daewoong Cheong, Thang Pham, Le Anh Vinh), Rev. Mat. Iberoam. 37 (2021), no. 4, 1365-1398. 

41. A sharp exponent on sum of distance sets over finite fields, (joint work with Thang Pham, Chun-Yen Shen, and Le Anh Vinh), Math. Z. 297 (2021), no. 3-4, 1749-1765.

40. Moderate Expanders Over Rings, (joint work with Dao Nguyen Van Anh, Le Quang Ham, Mozhgan Mirzaei, and Thang Pham), J. Number Theory 218 (2021), 223-233.

39. On a theorem of Hegyvari and Hennecart, (joint work with Dao Nguyen Van Anh, Le Quang Ham, Thang Pham, and Le Anh Vinh ), Pacific J. Math. 305 (2020), no. 2, 407-421. 

38. Exponential sum estimates over prime fields, (joint work with Mozhgan Mirzaei, Thang Pham, and Chun-Yen Shen), Int. J. Number Theory 16 (2020), no. 2, 291-308. 

37. Finite field restriction estimates for the paraboloid in high even dimensions, (joint work with Mark Lewko and Alex Iosevich), J. Funct. Anal, 278 (2020), no. 11, 108450. 

36. A new bound on Erdos distinct distances problem in the plane over prime fields, (joint work with Alex Iosevich, Thang Pham, Chun-Yen Shen, Le Anh Vinh), Acta Arith. 193 (2020), no. 2, 165-174. 

35. New bounds for distance-type problems over prime fields, (joint work with Alex iosevich and Thang Pham), European J. Combin. 86 (2020), 103080, PP. 1-11. 

34. Conjecture and improved extension theorems for paraboloids in the finite field setting, Math.Z. 294, (2020) 1-2, 51-69. 

33. Distance sets over arbitrary finite fields, (joint work with Sujin Lee, Thang Pham, and Chun-Yen Shen), Illinois J. Math., 63 (2019), no. 3, 469-484. 

32. On the determinants and permanents of matrices with restricted entries over prime fields , (joint work with Thang Pham, Chun-Yen Shen, and Le Anh Vinh), Pacific J. Math. 300 (2019), no. 2, 405-417. 

31.Expanding phenomena over matrix rings, (joint work with Yesim Demiroglu Karabulut, Thang Pham, Chun-Yen Shen, and Le Anh Vnh), Forum Math. 31 (2019), no. 4, 951-970. 

30. On the quotient set of the distance set, (joint work with Alex Iosevich and Hans Parshall), Mosc. J. Comb. Number Theory 8 (2019), no. 2, 103-115. 

29. The generalized k-resultant modulus set problem in finite fields, (joint work with David Covert and Youngjin Pi), J. Fourier Anal. Appl. 25 (2019), no. 3, 1026-1052. 

28. Expansion for the product of matrices in groups, (joint work with Thang Pham, Chun-Yen Shen, and Le Anh Vinh), Forum Math. 31 (2019), no. 1, 35-48. 

27. Restricted averaging operators to cones over finite fields, (joint work with Chun-Yen Shen and Seongjun Yeom), Forum Math. 30 (2018), no. 6, 1345-1361. 

26. Four-variable expanders over the prime fields, (joint work with Hossein Nassajian Mojarrad, Thang Pham, and Claudiu Valculescu, Proc. Amer. Math. Soc. 146 (2018), no. 12, 5025-5034. 

25. L^p-L^r estimates for k-plane transforms in finite fields, (joint work with Dongyoon Kwak), Proc. Amer. Math. Soc., 146 (2018), no. 8, 3381-3391. 

24. The k-resultant modulus set problem on algebraic varieties over finite fields, (joint work with David Covert and Youngjin Pi), Finite Fields Appl. 48 (2017), 68-86. 

23. Restricted averaging problems to algebraic varieties in finite fields (joint work with Seongjun Yeom), Taiwanese J. Math, 21 (2017), no.1, 211-229. 

22. Averaging operators over homogeneous varieties over finite fields , (joint work with Chun-Yen Shen and Igor Shparlinski), The Journal of Geometric Analysis, 26 (2016), no.2, 1415-1441. 

21. On the sums of any k points in finite fields, (joint work with David Covert and Youngjin Pi), SIAM J. Discrete Math, 30 (2016), no.1, 367-382. 

20. Sharp L^p- L^r estimates of restricted averaging operators over curves on planes in finite fields, Journal of the Chungcheong Mathematical Society, Volume 28(2015), no. 2, 251-259. 

19. Distance sets determined by two sets in vector spaces over finite fields, ( joint work with Hae-Sang Sun), Proc. Amer. Math. Soc. 143 (2015), no. 4, 1679-1692. 

18. Averaging operators over nondegenerate quadratic surfaces in finite fields, Forum Math., 27 (2015), 1227-1247. 

17. Weak version of restriction estimates for spheres and paraboloids in finite fields, (joint work with Hunseok Kang), J. Math. Anal. Appl., 419 (2014) 783-795. 

16. Restriction operators acting on radial functions on vector spaces over finite fields, Canad. Math. Bull. 57 (2014), no. 4, 834-844. 

15. Size of dot product sets determined by pairs of subsets of vector spaces over finite, (joint work with Yongjin Pi), Journal of the Chungcheong Mathematical Society, Volume 26(2013), no. 4, 853-867. 

14. Additive energy and the Falconer distance problem in finite fields ( joint work with Chun-Yen Shen), Integers, 13 (2013), A28 1-10. 

13. Distance graphs in vector spaces over finite fields(joint work with Derrick Hart, Alex Iosevich, Steve Senger and Ignacio Uriarte-Tuero), the Springer volume in honor of Kostya Oskolkov's 65th birthday, Recent Advances in Harmonic Analysis and Applications, Springer Proceedings in Mathematics and Statistics Volume 25, 2013, pp 139-160. 

12. Sharp endpoint estimates for the X-ray transform and the Radon transform in finite fields, Proc. Amer. Math. Soc. 141 (2013), no. 8, 2799-2808. 

11. Extension and averaging operators for finite fields ( joint work with Chun-Yen Shen), Proc. Edinb. Math. Soc. (2) 56 (2013), no. 2, 599-614. 

10. Harmonic analysis related to homogeneous varieties in three dimensional vector spaces over finite fields ( joint work with Chun-Yen Shen), Canad. J. Math. 64(2012), 1036-1057 Published:2011-12-23 (Printed: Oct 2012). 

9. The generalized Erdos-Falconer distance problems in vector spaces over finite fields ( joint work with Chun-Yen Shen) , Journal of Number Theory 132(2012),no.11, 2455-2473 (Printed: November 2012). 

8. Pinned distance sets, k-simplices, Wolff's exponent in finite fields and sum-product estimates ( joint work with J. Chapman, M. B. Erdogan, D. Hart, and A. Iosevich), Math. Z., Volume 271, June (2012), no.1, 63-93. 

7. Sharp extension theorems and Falconer distance problems for algebraic curves in two dimensional vector spaces over finite fields ( joint work with Chun-Yen Shen) , Revista Matematica Iberoamericana, Volume 28(2012), no.1, 157-178. 

6. Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdos-Falconer distance conjecture ( joint work with D. Hart, A. Iosevich, and M. Rudnev), Trans. Amer. Math. Soc. Volume 363, June (2011), no.6, 3255-3275. 

5. Extension theorems for paraboloids in the finite field setting ( joint work with Alex Iosevich), Math. Z. 266(2010), no.2, 471-487. 

4. Extension theorems for spheres in the finite field setting ( joint work with Alex Iosevich), Forum Math. 22 (2010), no. 3, 457-483. 

3. Generalized incidence theorems, homogeneous forms and sum-product estimates in finite fields ( joint work with D. Covert, D. Hart, A. Iosevich, and M. Rudnev ), European J. Combin. 31 (2010), no. 1, 306-319.

2. Extension theorems for the Fourier transform associated with nondegenerate quadratic surfaces in vector spaces over finite fields ( joint work with Alex Iosevich), Illinois J. Math. 52 (2008), no. 2, 611-628.

1. The Erdos-Falconer distance problem, exponential sums, and Fourier analytic approach to incidence theorems in vector spaces over finite fields ( joint work with Alex Iosevich), SIAM J. Discrete Math. 23 (2008/09), no. 1, 123-135 .

1.  The Erdős-Falconer distance problem between arbitrary sets and -coordinatable sets in finite fields, (joint work with Hunseok Kang and Firdavs Rakhmonov),   submitted  for publication,  (2025).