Associate
Professor
Dept. Mathematics
HKUST,
Clear Water Bay, Kowloon
Email:mamsxiong@ust.hk
Phone: 2358-7456 Office: 3477
Education and
Professional Experience
2016--Present:
Associate Professor, Dept. Mathematics, HKUST
2010--2016:
Assistant Professor, Dept. Mathematics, HKUST
2007--2010: S.
Chowla Assistant
Professor, Dept. Mathematics, Pennsylvania State University
2007, PhD., Dept.
Mathematics, University
of
Illinois at Urbana-Champaign
1999--2002,
Research Assistant,
University of
Science and Technology of China
1999, B.S.,
Mathematics, University
of
Science and Technology of China
Research Interests
Analytic number
theory. Elliptic curves. Additive combinatorics. Coding theory.
Publications
K. Feng and M.
Xiong, On
elliptic curves $y^2=x^3-n^2x$ with rank zero, J. Number
Theory
109 (2004), no. 1, 1--26. fx.pdf
M. Xiong and A.
Zaharescu, A
problem of Erdos-Szusz-Turan on Diophantine approximation,
Acta
Arith. 125 (2006), no. 2, 163--177. xz1.pdf
E. Alkan, M.
Xiong and A. Zaharescu, Local spacings along curves,
J. Math. Anal. Appl. 329 (2007), no. 1, 721--735. axz1.pdf
E. Alkan, M.
Xiong and A. Zaharescu, Arithmetic mean of differences of
Dedekind sums, Monatsh. Math. 151 (2007), no. 3, 175--187. axz3.pdf
E. Alkan, M.
Xiong and A. Zaharescu, A bias phenomenon on the behavior of
Dedekind sums, Math. Res. Lett. 15 (2008), no. 5, 1039--1052.
E. Alkan, M.
Xiong, A. Zaharescu, Quotients of values of the Dedekind Eta
function, Math. Ann. 342 (2008), no. 1, 157--176. axz5.pdf
M. Xiong, A.
Zaharescu, Distribution of Selmer groups of quadratic twists
of a family of elliptic curves, Adv. Math. 219 (2008), no. 2,
523--553. xz3.pdf
M. Xiong, A.
Zaharescu, Pair correlation of rationals with prime
denominators, J. Number Theory, 12 (2008), no. 10,
2795--2807. xz5.pdf
M. Xiong, The
Erdös-Kac theorem for polynomials of several variables, Proc.
Amer. Math. Soc. 137 (2009), no. 8, 2601--2608. x1.pdf
M. Xiong and A.
Zaharescu, Selmer groups and Tate-Shafarevich groups for the
congruent number
problem, Comment. Math. Helv. 84 (2009), no. 1, 21--56. xz2.pdf
E. Alkan, M.
Xiong, A. Zaharescu, Pair correlation of torsion points on
elliptic curves, J. Math. Anal. Appl. 356 (2009), no. 2,
752--763. axz22.pdf
Nicholas Katz,
I.E. Shparlinski, M. Xiong, On character sums with distances
on the upper half plane over a finite field, Finite Fields
Appl. 15 (2009), no. 6, 738--747. sx.pdf
A. Iosevich, I.E.
Shparlinski and M. Xiong, Sets with integral distances in
finite fields, Trans. Amer. Math. Soc. 362 (2010), no. 4,
2189--2204. isx.pdf
E. Alkan, A.
Zaharescu, M. Xiong, Pair correlation of sums of rationals
with bounded height, J. Reine Angew. Math. 641 (2010),
21--67. axz2.pdf
M. Xiong, Statistics
of the zeros of zeta functions in a family of curves over a finite
field, International Mathematics Research Notices IMRN,
2010, 30 pages. x42.pdf
M. Xiong, The
fluctuations in the number of points on a family of curves over a
finite field, J. Theor. Nombres Bordeaux 22 (2010), no. 3,
755--769. x3.pdf
M. Xiong, A.
Zaharescu, Correlation of fractions with divisibility
constraints, Math. Nachr. 284 (2011), no. 2-3, 393--407. xz4.pdf
M. Xiong, A.
Zaharescu, k-full integers between successive k-th powers,
Indag. Math. 22 (2011), no. 1-2, 77--86.
M. Xiong, A.
Zaharescu, Statistics of the Jacobians of hyperelliptic
curves over finite fields, Math. Res. Lett. 19 (2012), no. 2,
255--272.
K. Feng, M.
Xiong, On Selmer groups and Tate-Shafarevich groups for
elliptic curves $y^2=x^3-n^3$, Mathematika 58 (2012), no. 2,
236--274.
M. Xiong, A.
Zaharescu, Pair correlation of latrice points with prime
constraint, Acta Arith. 154 (2012), 29--43.
M. Xiong, On
Selmer groups of quadratic twists of elliptic curves with a two-torsion
over Q, Mathematika 59 (2013), no. 2, 303--319.
M. Xiong, The
weight distributions of a class of cyclic codes, Finite
Fields Appl. 18 (2012), 933--945.
M. Xiong, The
weight distributions of a class of cyclic codes II, Des.
Codes Cryptogr. 72 (2014), no. 3, 511--528.
M. Xiong, The
weight distributions of a class of cyclic codes III, Finite
Fields Appl. 21 (2013), 84--96.
J. Yang, M.
Xiong, C. Ding, J. Luo, Weight distribution of a class of
cyclic codes with arbitrary number of zeros, IEEE Trans.
Infor. Theory 59 (2013), no. 9, 5989--5993.
Z. Zhou, A.
Zhang, C. Ding, M. Xiong, The weight enumerator of three
families of cyclic codes, IEEE Trans. Infor.
Theory 59 (2013),
no. 9, 6002--6009.
C. Ding, K. Feng,
R. Feng, M. Xiong, A. Zhang, Unit time-phase signal sets:
Bounds and constructions, Cryptogr. Commun. 5
(2013), no. 9, 209--222.
C. Ding, Q. Wang,
M.
Xiong, Three new families of zero-difference balanced
functions with applications. IEEE
Trans. Infor. Theory 60 (2014), 2407--2413.
J.Xia and M.
Xiong, On a question of Babadi and Tarokh, IEEE
Trans. Infor. Theory 60 (2014), no. 11, 7355--7367.
M. Xiong, On
positive proportion of rank zero twists of elliptic curves over Q,
J.
Aust. Math. Soc. 98 (2015), no. 2, 281--288.
M. Xiong,
Distribution of zeta zeroes for abelian covers of
algebraic curves over
a finite field, J. Number Theory 147 (2015), 789--823.
J. Yang, M.
Xiong, L. Xia, Weight distributions of a class of cyclic
codes with
arbitrary number of nonzeros in quadratic case, Finite Fields
Appl. 36
(2015), 41--62.
M. Xiong, N. Li,
Z. Zhou, C. Ding, Weight distribution of cyclic codes with
arbitrary
number of generalized Niho type zeroes, to appear in Des.
Codes
Cryptogr. DOI 10.1007/s10623-014-0027-5.
M. Xiong, N. Li, Optimal
cyclic codes with generalized Niho type zeroes and the weight
distribution, IEEE Trans. Inform. Theory 61 (2015), no. 9,
4914--4922.