Preprints & Articles Under Review
- Level
17 Ramanujan-Sato Series, with D. Schultz and Dongxi Ye
Not yet Submitted.
- Series
for 1/Pi of Signature 20, with D. Schultz and Dongxi Ye
Not yet Submitted.
- The distribution of zeros for Laurent coefficients of the Jacobi elliptic functions,
Not yet Submitted.
Publications
- Balanced Modular Parameterizations, (with students D. Lara and E. Melendez)
Frontiers in Orthogonal Polynomials and q-Series, World
Scientific, To Appear 2017.
- Weierstrass interpolation of Hecke Eisenstein series, (with student M. Levine),
The Mathematics Student, Indian Mathematical Society, Vol. 86, No. 1-2, January-June, 2017.
- Generalized Reciprocal
Identities, (with Daniel Schultz)
Proceedings of the American Mathematical Society, Volume 144,
Number 11, Pages 4627–4639, , November 2016.
- Differential equations for septic theta functions, (with student D. Lara),
Ramanujan Journal, Volume 38, Issue 1, pp 211-226, 2015.
- On cubic multisections of Eisenstein series, (with student A. Alaniz),
The Ramanujan Journal, Volume 35, Issue 3, pp 391-403, 2014.
- A theory of theta functions to the quintic base,
Journal of Number Theory, Volume 134, pp. 49-92, 2014.
- Parameterizations for quintic Eisenstein series, (with students R. Charles and A. Mendoza),
Journal of Number Theory, Volume 133, Number 1, pp. 195-214, 2013.
- On quintic Eisenstein series and points of order five of the Weierstrass elliptic functions,
The Ramanujan Journal, Volume 28, Issue 2, pp. 273-308, 2012.
- Differential equations for cubic theta functions,
International Journal of Number Theory, Volume 7, Number 6, pp. 1-12, 2011.
- Zeros of generalized Rogers-Ramanujan series:
Asymptotic and combinatorial properties,
Journal of Approximation Theory, Volume 162, Issue 5, pp. 910-930, 2010.
- Combinatorics of Generalized q-Euler Numbers, (with A. J. Yee),
Journal of Combinatorial Theory, Series A, Volume 117, Issue 4, pp. 361-388, 2010.
- Coupled systems of differential equations for modular forms of level n,
Ramanujan Rediscovered, Ramanujan Mathematical Society, Lecture Note Series, 2010.
- Basic representations for Eisenstein series from their differential equations,
Journal of Mathematical Analysis and Applications, Volume 350, Issue 1, pp. 135-146, 2009.
- Hadamard products for generalized Rogers-Ramanujan series,
Journal of Approximation Theory, Volume 151, Number 2, pp.~126--154, 2008.
- A fragment on Euler's constant in Ramanujan's Lost Notebook, (with B. C. Berndt),
South East Asian J. Math. Sci., Volume 6, No. 2, pp. 17-22, 2008.
- Solving Ramanujan's differential relations for Eisenstein series via a first order Riccati equation, (with J. Hill and B. C. Berndt),
Acta Arithmetica, Volume 128, No. 3, pp. 281--294, 2007.
- Zeros of Generalized Rogers-Ramanujan Series and Topics from Ramanujan's Theory of Elliptic Functions.
Ph. D. Thesis, University of Illinois at Urbana-Champaign, 2007.
Snippets for Papers Under Preparation
- Congruences for septic theta functions,
Not yet Submitted.
- Symmetric Septic Forms for Eisenstein Series, (with student E. Melendez),
Not yet Submitted.
- Generators for Eisenstein series of level eleven,
Not yet Submitted.