Ling Long

Associate Professor

Ph.D. Pennsylvania State University, 2002

Contact: 256 Lockett Hall, (225)-578-1677, llongATlsu.edu

Teaching (Fall 2013) Math2057 sections 5&6: Syllabus

Reserach Interests: Number Theory and Applications

Conference Organizer:

Applications of Automorphic Forms in Number Theory and Combinatorics, Baton Rouge, Louisiana, April 12-15, 2014
Banff International Research Station (BIRS), Women in Numbers 3, April 2014
Special Session at AMS sectional meeting at Iowa city, March 18-20 2011
American Institute for Mathematics (AIM) week long workshop on Noncongruence modular forms and modularity, August 2009.
Special Session at AMS Joint Meeting at San Diego, January 2008.

Major Research Grants and Scholarship:

NSF research grant DSM#1303292, PI, 2013-2016
NSF conference grant DSM#1363265, PI 2013-2014
AWM Ruth I. Michler Memorial Prize 2012-2013 winner
NSF research grant, PI, 2010-2013
NSA Young Investigators Grant, PI, 2008-2010
Clay Mathematical Institute: Liftoff Research Fellowship, 2002

Publications:

Supercongruences and Complex Multiplication, (with Jonas Kibelbek, Kenvin Moss, Benjamin Sheller, Hao Yuan), arXiv:1210.4489, Journal of Number Theory, accepted subject to modification, (2013)
p-adic analogues of Ramanujan type formulas for 1 over Pi, (with Sarah Chisholm, Alyson Deines, Gabriele Nebe, and Holly Swisher), Mathematics, vol 1, (2013)
Galois representations with quaternion multiplications associated to noncongruence modular forms, (with A.O.L. Atkin, Wen-Ching Winnie Li, and Tong Liu), arXiv:1005.4105, Trans. of Ameri. Soc., to appear.
On l-adic representations for a space of noncongruence cuspforms, (with Jerome William Hoffman and Helena Verrill), Proc. Amer. Math. Soc., 140 (2012), 1569-1584.
Fourier coefficients of noncongruence cuspforms, (with Wen-Ching Winnie Li), Bull. London Math. Soc. (2012) doi: 10.1112/blms/brd112
Hypergeometric evaluation identities and supercongruences, Pacific J. of Math, 249-2 (2011), 405--418.
Jacobsthal identity for $\Q(\sqrt{-2})$, (with Ki-Ichiro Hashimoto and Yifan Yang), Forum Mathematicum, Forum Mathematicum, Volume 24, Issue 6, 1225-1238, (2012)
Zeros of classical Eisenstein series and recent developments, (with Sharon Garthwaite, Holly Swisher, Stephanie Treneer), Fields Communications Volume 60, WIN - Women In Numbers, Proceedings of the WIN Workshop, (2011), 251-263.
Zeros of classical Eisenstein series and recent developments, (with Sharon Garthwaite, Holly Swisher, Stephanie Treneer), Fields Communications Volume 60, WIN - Women In Numbers, Proceedings of the WIN Workshop, (2011), 251-263.
A cubic analogue of the Jacobsthal identity, (with Heng-Huat Chang and Yifan Yang) , Math. Monthly, 118:4 (2010), 316-326.
A supercongruence motivated by the Legendre family of elliptic curves, (with Heng-Huat Chang and Wadim Zudilin) Mathematical Notes, Vol. 88, No. 4, pp. 599–602, (2010)
Catalan loops, (with Jonathan D. H. Smith), Mathematical Proceedings of Cambridge Philosophical Society, Vol. 149, 445-453, (2010).
Zeros of some level 2 Eisenstein series (with Sharon Garthwaite, Holly Swisher, Stephanie Treneer), Proc. Amer. Math. Soc., 138 (2010), 467-480.
On modular forms for some noncongruence subgroups of the modular group II, (with Chris Kurth), Bull. London Math. Soc. (2009), Vol. 41 589-598; doi:10.1112/blms/bdp061
On Atkin and Swinnerton-Dyer congruence relations (3), Journal of Number Theory, Vol. 128 No. 8, (2008) 2413-2429
Computations with finite index subgroups of PSL2(Z) using Farey Symbols, (with Chris Kurth), Advances in Algebra and Combinatorics, Proceedings of the Second International Congress in Algebra and Combinatorics, World Scientific, (2008) 225-242.
On modular forms for some noncongruence subgroups of the modular group, (with Chris Kurth), Journal of Number Theory, Vol. 128 No. 7 (2008) 1989-2009.
Finite index subgroups of the modular group and their modular forms, Modular Forms and String Duality, Fields Institute Communications, Vol. 54, (2008) 83-102
On Atkin and Swinnerton-Dyer congruence relations (2) (with A.O.L. Atkin and Wenching Winnie Li), Mathematische Annalen, Vol. 340, No.2 (2008) 335-358.
Reciprocity for Stirling and multi-restricted numbers (with Ji Young Choi, Siu-Hung Ng and Jonathan Smith), Journal of Combinatorial Theory, Series A, Vol.113 (2006) 1050-1060.
A short proof of Milne’s formulae for sums of integer squares, (with Yifan Yang), International Journal of Number Theory, Vol. 1 no. 4 (2005) 533-551.
On Atkin and Swinnerton-Dyer congruence relations, (with Wen-Ching W.Li and Zifeng Yang), Journal of Number Theory, Vol. 113, No.1 (2005) 117-148.
Modular forms for noncongruence subgroups, (with Wen-Ching W. Li and Zifeng Yang), Quarterly Journal of Pure and Applied Mathematics, Vol. 1, No.1, 205-221, 2005.
On Shioda-Inose structures of one parameter families of K3 surfaces, Journal of Num-ber Theory, 2004, Vol.109, No.2 (2004) 299-318.
L-series of certain elliptic surfaces, Canadian Mathematical Bulletin, Vol. 46, No.4 (2003), 546-558.
On a Shioda-Inose structure of a family of K3 surfaces, Calabi-Yau Varieties and Mir-ror Symmetry, Fields Institute Communications 38, American Mathematica Society, Providence RI (2003) 201-207.