## Min Sha

 Telephone: +61-(0)93855827 Email: Office: Room 4074, Centre Wing of the Red Centre

Brief Introduction:

I am currently a Postdoctoral Fellow at the University of New South Wales under the supervision of Prof. Igor E. Shparlinski. My main interest is number theory and its applications. For more information, please visit my CV.

Papers/Preprints:

·  k-Error linear complexity of multidimensional arrays, preprint, 2016. (with Domingo Gómez-Pérez and Andrew Tirkel)

·  On multiplicatively dependent vectors of algebraic numbers, preprint, 2016. (with Francesco Pappalardi, Igor E. Shparlinski and Cameron Stewart)

·  On two functions arising in the study of the Euler and Carmichael quotients, preprint, 2016. (with Florian Luca and Igor E. Shparlinski)

·  On distances in lattices from algebraic number fields, preprint, 2016. (with Artūras Dubickas and Igor E. Shparlinski)

·  Corrigendum to “On the quantitative dynamical Mordell-Lang conjecture”, Journal of Number Theory, 164 (2016), 433-437. (with Alina Ostafe)

·  Gauss factorials of polynomials over finite fields, preprint, 2015. (with Xiumei Li)

·  The Sato-Tate distribution in families of elliptic curves with a rational parameter of bounded height, preprint, 2015. (with Igor E. Shparlinski)

·  The Sato-Tate distribution in thin parametric families of elliptic curves, preprint, 2015. (with Régis de la Bretèche, Igor E. Shparlinski and José Voloch)

·  The arithmetics of consecutive polynomial sequences over finite fields, preprint, 2015. (with Domingo Gómez-Pérez and Alina Ostafe)

·  On the decision problems of linear recurrence sequences, preprint, 2015.

·  Positive density of integer polynomials with some prescribed properties, Journal of Number Theory, 159 (2016), 27-44. (with Artūras Dubickas)

·  Counting dynamical systems over finite fields, Contemporary Mathematics, to appear. (with Alina Ostafe)

·  On the quantitative dynamical Mordell-Lang conjecture, Journal of Number Theory, 156 (2015), 161-182. (with Alina Ostafe)

·  Pseudolinearly dependent points on elliptic curves, preprint, 2014. (with Igor E. Shparlinski)

·  Experimental Mathematics, 24 (2015), 312-325. (with Artūras Dubickas)

·  On the lattices from elliptic curves over finite fields, Finite Fields and Their Applications, 31 (2015), 84-107.

·  Lang-Trotter and Sato-Tate distributions in single and double parametric families of elliptic curves, Acta Arithmetica, 170 (2015), 299-325. (with Igor E. Shparlinski)

·  Counting degenerate polynomials of fixed degree and bounded height, Monatshefte für Mathematik, 177 (2015), 517-537. (with Artūras Dubickas)

·  Explicit form of Cassels' p-adic embedding theorem for number fields, Canadian Journal of Mathematics, 67 (2015), 1046-1064. (with Artūras Dubickas and Igor E. Shparlinski)

·  Functional graphs of polynomials over finite fields , Journal of Combinatorial Theory, Series B, 116 (2016), 87--122. (with Sergei V. Konyagin, Florian Luca, Bernard Mans, Luke Mathieson and Igor E. Shparlinski)

·  On the non-idealness of cyclotomic families of pairing-friendly elliptic curves, Journal of Mathematical Cryptology, 8 (2014), 417-440.

·  Bounding the j-invariant of integral points on certain modular curves, International Journal of Number Theory, 10(6) (2014), 1545-1551.

·  The arithmetic of Carmichael quotients, Periodica Mathematica Hungarica, 71 (2015), 11-23.

·  Bounding the j-invariant of integral points on modular curves, International Mathematics Research Notices, 2014 (16) (2014), 4492-4520.

·  Bounding the j-invariant of integral points on $X_{\ns}^{+}(p)$, Proceedings of the American Mathematical Society, 142 (2014), 3395-3410. (with Dr. Aurélien Bajolet)

·  Heuristics of the Cocks-Pinch method, Advances in Mathematics of Communications 8 (2014), 103-118.

·  Digraphs from endomorphisms of finite cyclic groups, Journal of Combinatorial Mathematics and Combinatorial Computing, 83 (2012), 105-120.

·  Galois groups and genera of a kind of quasi-cyclotomic function fields, Journal of Number Theory, 132 (2012), 2574-2581. (with Prof. Linsheng Yin)

·  Monomial dynamical systems of dimension one over finite fields, Acta Arithmetica, 148 (2011), 309-331. (with Dr. Su Hu)

·  On the cycle structure of repeated exponentiation modulo a prime power, Fibonacci Quarterly, 49 (2011), 340-347