Ling Long

Publications: Google Scholar

Preprints:

  • Traces of Hecke Operators via Hypergeometric Character Sums, (with Jerome W. Hoffman, Wen-Ching Winnie Li, and Fang-Ting Tu) arXiv:2408.02918 (2024)
  • Hodge numbers of hypergeometric data, (with Yifan Yang), arxiv:2404.02834 (2024).
  • The Explicit Hypergeometric-Modularity Method, (with Michael Allen, Brian Grove, and Fang-Ting Tu), Part I arxiv:2404.00711 , Part II arxiv:2411.15116 (2024).

    • Published:

  • Hypergeometric functions over finite fields, (with Jenny G. Fuselier, Ravi Ramakrishna, Holly Swisher, and Fang-Ting Tu), arxiv:1510.02575 , Memoirs of the AMS, 280 (2022), no 1382
  • A Whipple $_7F_6(1)$ formula revisited (with Wen-Ching Winnie Li and Fang-Ting Tu), La Mathematica, article/10.1007/s44007-021-00015-6, arXiv:2103.08858 (2022)
  • Supercongruences for rigid hypergeometric Calabi--Yau threefolds (with Fang-Ting Tu, Noriko Yui, Wadim Zudilin), Adv. in Math. 393 Article 108058 (2021), arXiv:1705.01663
  • Some Numeric Hypergeometric Supercongruences, arxiv.org:1812.07560. Some numeric hypergeometric supercongruences. Vertex operator algebras, number theory and related topics, 139–156, Contemp. Math., 753, Amer. Math. Soc., Providence, RI, 2020.
  • Computing Special L-values of Certain Modular Forms with Complex Multiplication (with Wen-Ching Winnie Li and Fang-Ting Tu) arXiv:1803.06072 , SIGMA 14 (2018), 090, 32 pages
  • Potentially $GL_2$-type Galois representations associated to noncongruence modular forms (with Wen-Ching Winnie Li and Tong Liu), arxiv:1609.06414, Trans. of AMS, 371 (2019), 5341-5377.
  • Characterization of intersecting families of maximum size in $PSL(2,q)$ (with Rafael Plaza, Peter Sin, and Qing Xiang), Journal of Combinatorial Theory, Series A Vol. 157 (2018) 461-499, arxiv:1608.07304
  • Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions, (with Alyson Deines, Jenny G. Fuselier, Holly Swisher, and Fang-Ting Tu), arxiv:1501.03564, Directions in number theory, 125–159, Assoc. Women Math. Ser., 3, Springer, 2016.
  • On a conjecture of Kimoto and Wakayama, (with Robert Osburn, Holly Swisher), arXiv:1404.4723, Proc. Amer. Math. Soc. 144 (2016), no. 10, 4319–4327.
  • Supercongruences and Complex Multiplication, (with Jonas Kibelbek, Kenvin Moss, Benjamin Sheller, Hao Yuan), arXiv:1210.4489, Journal of Number Theory, Volume 164, 166-178, 2016.
  • Generalized Legendre curves and Quaternionic Multiplication, (with Alyson Deines, Jenny G. Fuselier, Holly Swisher, and Fang-Ting Tu) arXiv:1412.6906 Journal of Number Theory, 161, 175-203, 2016.
  • Some supercongruences occurring in truncated hypergeometric series (with Ravi Ramakrishna), arXiv:1403.5232 Adv. in Math. 290, 773-808, 2016.
  • Preface (with Jerome Hoffman, Karl Mahlburg, Jorge Morales, Bogdan Oporowski, Robert Perlis, Holly Swisher), J. Number Theory 161, 1-16, 2016.
  • Atkin and Swinnerton-Dyer congruences and noncongruence modular forms (with Wen-Ching Winnie Li), arXiv:1303.6228, RIMS Kokyuroku Bessatsu, B51 (2014), 269-299.
  • 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. Amer. Math. Soc. 365 (2013), no. 12, 6217–6242.
  • 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)
  • Jacobsthal identity for $\Q(\sqrt{-2})$, (with Ki-Ichiro Hashimoto and Yifan Yang), Forum Mathematicum, Volume 24, Issue 6, 1225-1238, (2012)
  • Hypergeometric evaluation identities and supercongruences, Pacific J. of Math, 249-2 (2011), 405--418.
  • 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
  • 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 Number 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.
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