教师个人简历

沙敏个人简历
基本资料
姓    名：
沙敏
英 文 名：
Min Sha
性    别：
男
出生年月：
1983年10月
籍    贯：
广东龙川
学    位：
博士
职    称：
副研究员
研究领域：
数论及其应用
联系方式：
数学科学学院西楼105办公室，shamin@scnu.edu.cn
工作经历
教育经历：
2003.9--2007.7  华南理工大学  本科 （数学与应用数学） 
2007.9--2010.7  清华大学  硕士（基础数学：数论）
2010.9--2013.10   法国波尔多大学  博士（基础数学：数论） 

工作经历：
2013.12.2--2016.6.26 澳大利亚新南威尔士大学数学与统计学院  Postdoctoral Fellow
2016.6.27--2019.3.31 澳大利亚麦考瑞大学计算机系  Macquarie University Research Fellow
2019.4.1--2020.7.10 澳大利亚新南威尔士大学数学与统计学院  Research Fellow
2020.7.29--  华南师范大学数学科学学院  副研究员

科研项目：
1. 国家自然科学基金青年科学基金项目，p-进模形式与类域构作问题，2016.1--2018.12，参加。
2. 广东省自然科学基金面上项目，Mertens定理的一般形式，2019.10--2022.9，参加。
3. 澳大利亚研究理事会Discovery Early Career Researcher Award项目，DE190100888，Linear recurrence sequences over function fields and their applications，2019.4--2022.4，主持，因为回国工作项目已经终止。
 
科研成果
研究兴趣广泛，涉及代数数论、椭圆曲线、有限域理论、多项式理论、算术动力系统、线性递归序列、数论中的图论问题等等。研究成果丰富，至今发表了40余篇SCI论文，发表的期刊包括：Trans Amer Math Soc, Int Math Res Notices, J Comb Theory B, Math Zeit, Moscow Math J, Canadian J Math, Rev Mat Iberoam, Proc Amer Math Soc, Bull London Math Soc, J Algebra, J Number Theory, Acta Arith, Finite Fields Th App, J Complexity等国际知名期刊。
科研论文
  1. F. Barroero, L. Capuano, L. Merai, A. Ostafe and M. Sha,   Multiplicative and linear dependence in finite fields and on elliptic curves  modulo primes, International Mathematics Research Notices, https://doi.org/10.1093/imrn/rnab171.  https://arxiv.org/abs/2008.00389
  2. M. Sha, Zsigmondy's theorem and primitive divisors of the Lucas and Lehmer sequences in polynomial rings,  Journal of Algebra, 586 (2021), 830-843. https://arxiv.org/abs/2005.01940
  3. M. Sha and I.E. Shparlinski, Mobius randomness law for Frobenius traces of ordinary curves, Canadian Mathematical Bulletin, 64 (2021), 192-203. https://arxiv.org/abs/1909.00969
  4. F. Barroero and M. Sha, Torsion points with multiplicatively dependent coordinates on elliptic curves, Bulletin of the London Mathematical Society, 52 (2020), 807-815. https://arxiv.org/abs/1904.02474
  5. X. Li and M. Sha, A proof of Sondow's conjecture on the Smarandache function, The American Mathematical Monthly, 127 (2020), 939-943. https://arxiv.org/abs/1907.00370
  6. X. Li and M. Sha, Polynomial analogue of the Smarandache function, Journal of Number Theory, 217 (2020), 320-339. https://arxiv.org/abs/1906.00510
  7. B. Mans, M. Sha, J. Smith and D. Sutantyo, On the equational graphs over finite fields, Finite Fields and Their Applications, 64 (2020), Article 101667. https://arxiv.org/abs/1906.12054
  8. X. Li and M. Sha, Congruence preserving functions in the residue class rings of polynomials over finite fields, Finite Fields and Their Applications, 61 (2020), Article 101604. https://arxiv.org/abs/1807.02379
  9. S. Hu, M. Kim, P. Moree and M. Sha, Irregular primes with respect to Genocchi numbers and Artin's primitive root conjecture, Journal of Number Theory, 205 (2019), 59-80. https://arxiv.org/abs/1809.08431
  10. P. Moree and M. Sha, Primes in arithmetic progressions and nonprimitive roots, Bulletin of the Australian Mathematical Society, 100 (2019), 388-394. https://arxiv.org/abs/1901.02650
  11. X. Li and M. Sha, Polynomial functions in the residue class rings of Dedekind domains, International Journal of Number Theory, 15 (2019), 1473-1486. https://arxiv.org/abs/1704.04965
  12. B. Mans, M. Sha, I.E. Shparlinski and D. Sutantyo, On functional graphs of quadratic polynomials, Experimental Mathematics, 28 (2019), 292-300. https://arxiv.org/abs/1706.04734
  13. A. Ostafe, M. Sha, I.E. Shparlinski and U. Zannier, On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem, Michigan Mathematical Journal, 68 (2019), 385-407. https://arxiv.org/abs/1706.05874
  14. S. Hu and M. Sha, On the additive and multiplicative structures of the exceptional units in finite commutative rings, Publicationes Mathematicae Debrecen, 94 (2019), 369-380. https://arxiv.org/abs/1612.04539
  15. M. Sha, Effective results on the Skolem Problem for linear recurrence sequences, Journal of Number Theory,  197 (2019), 228-249. https://arxiv.org/abs/1505.07147
  16. A. Dubickas and M. Sha, Multiplicative dependence of the translations of algebraic numbers, Revista Matematica Iberoamericana, 34 (2018), 1789-1808. https://arxiv.org/abs/1608.05458
  17. A. Dubickas and M. Sha, The distance to square-free polynomials, Acta Arithmetica, 186 (2018), 243-256. https://arxiv.org/abs/1801.01240
  18. D. Gomez-Perez, M. Sha and A. Tirkel, On the linear complexity for multidimensional sequences,  Journal of Complexity, 49 (2018), 46-55. https://arxiv.org/abs/1803.03912
  19. R. de la Breteche, M. Sha, I.E. Shparlinski and J.F. Voloch,  The Sato-Tate distribution in thin parametric families of elliptic curves, Mathematische Zeitschrift, 290 (2018), 831-855. https://arxiv.org/abs/1509.03009
  20. F. Pappalardi, M. Sha, I.E. Shparlinski and C. Stewart, On multiplicatively dependent vectors of algebraic numbers, Transactions of the American Mathematical Society, 370 (2018), 6221-6244. https://arxiv.org/abs/1606.02874
  21. A. Ostafe, M. Sha, I.E. Shparlinski and U. Zannier, On abelian multiplicatively dependent points on a curve in a torus, Quarterly Journal of Mathematics, 69 (2018), 391-401. https://arxiv.org/abs/1704.04694
  22. M. Sha and I.E. Shparlinski, Effective results on linear dependence for elliptic curves, Pacific Journal of Mathematics, 295 (2018), 123-144. https://arxiv.org/abs/1410.1596
  23. A. Dubickas and M. Sha, On the number of integer polynomials with multiplicatively dependent roots, Acta Mathematica Hungarica, 154 (2018), 402-428. https://arxiv.org/abs/1707.04965
  24. D. Gomez-Perez, A. Ostafe and M. Sha, The arithmetics of consecutive polynomial sequences over finite fields, Finite Fields and Their Applications, 50 (2018), 35-65. https://arxiv.org/abs/1509.01936
  25. A. Dubickas, M. Sha and I.E. Shparlinski, On distances in lattices from algebraic number fields, Moscow Mathematical Journal, 17 (2017), 239-268. https://arxiv.org/abs/1703.02163
  26. F. Luca, M. Sha and I.E. Shparlinski, On two functions arising in the study of Carmichael quotients, Colloquium Mathematicum, 149 (2017) , 179-192. https://arxiv.org/abs/1705.00388
  27. X. Li and M. Sha, Gauss factorials of polynomials over finite fields, International Journal of Number Theory, 8 (2017), 2039-2054. https://arxiv.org/abs/1704.04972
  28. M. Sha and I.E. Shparlinski, The Sato-Tate distribution in families of elliptic curves with a rational parameter of bounded height, Indagationes Mathematicae, 28 (2017), 306-320. https://arxiv.org/abs/1512.07301
  29. A. Ostafe and M. Sha, Counting dynamical systems over finite fields, Contemporary Mathematics, 669 (2016), 187-203. https://arxiv.org/abs/1505.03618
  30. S.V. Konyagin, F. Luca, B. Mans, L. Mathieson, M. Sha and I.E. Shparlinski, Functional graphs of polynomials over finite fields, Journal of Combinatorial Theory, Series B, 116 (2016), 87-122. https://arxiv.org/abs/1307.2718
  31. A. Dubickas and M. Sha, Positive density of integer polynomials with some prescribed properties, Journal of Number Theory, 159 (2016), 27-44. https://arxiv.org/abs/1504.05144
  32. M. Sha and I.E. Shparlinski, Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves, Acta Arithmetica, 170 (2015), 299-325. https://arxiv.org/abs/1404.0182
  33. A. Dubickas, M. Sha and I.E. Shparlinski, Explicit form of Cassels' p-adic embedding theorem for number fields, Canadian Journal of Mathematics, 67 (2015), 1046-1064. https://arxiv.org/abs/1401.6819
  34. A. Ostafe and M. Sha, On the quantitative dynamical Mordell-Lang conjecture, Journal of Number Theory, 156 (2015),  161-182. Corrigendum: Journal of Number Theory, 164 (2016), 433-437. https://arxiv.org/abs/1501.02543
  35. A. Dubickas and M. Sha, Counting and testing dominant polynomials, Experimental Mathematics, 24 (2015), 312-325. https://arxiv.org/abs/1407.2789
  36. M. Sha, On the lattices from elliptic curves over finite fields, Finite Fields and Their Applications, 31 (2015), 84-107. https://arxiv.org/abs/1406.3086
  37. M. Sha,  The arithmetic of Carmichael Quotients, Periodica Mathematica Hungarica, 71 (2015), 11-23. Corrigendum: Periodica Mathematica Hungarica, https://doi.org/10.1007/s10998-017-0227-7. https://arxiv.org/abs/1108.2579
  38. A. Dubickas and M. Sha, Counting degenerate polynomials of fixed degree and bounded height, Monatshefte fur Mathematik, 177 (2015), 517-537. https://arxiv.org/abs/1402.5430
  39. M. Sha, On the non-idealness of cyclotomic families of pairing-friendly elliptic curves, Journal of Mathematical Cryptology, 8 (2014), 417-440. https://arxiv.org/abs/1304.7169
  40. M. Sha, Heuristics of the Cocks-Pinch method, Advances in Mathematics of Communications, 8 (2014), 103-118. https://arxiv.org/abs/1211.0971
  41. M. Sha, Bounding the j-invariant of integral points on certain modular curves, International Journal of Number Theory, 10 (2014), 1545-1551. https://arxiv.org/abs/1210.3224
  42. M. Sha, Bounding the j-invariant of integral points on modular curves}, International Mathematics Research Notices, 2014 (2014), 4492-4520. https://arxiv.org/abs/1208.1337
  43. A. Bajolet and M. Sha, Bounding the j-invariant of integral points on X_{ns}^{+}(p), Proceedings of the American Mathematical Society, 142 (2014), 3395-3410. https://arxiv.org/abs/1203.1187
  44. M. Sha, Digraphs from endomorphisms of finite cyclic groups,  Journal of Combinatorial Mathematics and Combinatorial Computing, 83 (2012), 105-120. https://arxiv.org/abs/1007.1712
  45. M. Sha and L. Yin, Galois groups and genera of a kind of quasi-cyclotomic function fields}, Journal of Number Theory, 132 (2012), 2574-2581. https://arxiv.org/abs/1007.1729
  46. M. Sha and S. Hu, Monomial dynamical systems of dimension one over finite fields, Acta Arithmetica, 148 (2011), 309-331. https://arxiv.org/abs/0910.5550
  47. M. Sha, On the cycle structure of repeated exponentiation modulo a prime power, Fibonacci Quarterly, 49 (2011), 340-347. https://arxiv.org/abs/1101.3482
     
更多
Preprints: 
  1. A. Dubickas and M. Sha, Counting decomposable polynomials with integer coefficients, preprint, 2021, https://arxiv.org/abs/1803.08755.
  2. A. Berczes, J. Mello, A. Ostafe and M. Sha, Multiplicative dependence of rational values modulo approximate finitely generated groups,  preprint, 2021, https://arxiv.org/abs/2107.05371.   
  3. J. Mello and M. Sha, On the properties of Northcott and Narkiewicz for elliptic curves, preprint, 2021,  https://arxiv.org/abs/1911.08752.  
  4. M. Sha, On the Lucas and Lehmer sequences in transcendental Dedekind domains, preprint, 2021, https://arxiv.org/abs/2006.09880.  
  5. S. V. Konyagin, M. Sha, I. E. Shparlinski and C. L. Stewart, On the distribution of multiplicatively dependent vectors, preprint, 2021,  https://arxiv.org/abs/1903.09796.  
  6. S. Hu, M. Kim and M. Sha, On the congruences of Eisenstein series with polynomial indexes, preprint, 2021, https://arxiv.org/abs/1805.09225.
  7. S. Bae, S. Hu and M. Sha, On the Carmichael rings, Carmichael ideals and Carmichael polynomials, preprint, 2019,  https://arxiv.org/abs/1809.05432.