N-soliton Gilbarg proposition proposition

Preprints & Articles Under Review

  1. Level 17 Ramanujan-Sato Series, with D. Schultz and Dongxi Ye
    Not yet Submitted.

  2. Series for 1/Pi of Signature 20, with D. Schultz and Dongxi Ye
    Not yet Submitted.

  3. The distribution of zeros for Laurent coefficients of the Jacobi elliptic functions,
    Not yet Submitted.

Publications

  1. Balanced Modular Parameterizations, (with students D. Lara and E. Melendez)
    Frontiers in Orthogonal Polynomials and q-Series, World Scientific, To Appear 2017.

  2. Weierstrass interpolation of Hecke Eisenstein series, (with student M. Levine),
    The Mathematics Student, Indian Mathematical Society, Vol. 86, No. 1-2, January-June, 2017.

  3. Generalized Reciprocal Identities, (with Daniel Schultz)
    Proceedings of the American Mathematical Society, Volume 144, Number 11, Pages 4627–4639, , November 2016.

  4. Differential equations for septic theta functions, (with student D. Lara),
    Ramanujan Journal, Volume 38, Issue 1, pp 211-226, 2015.

  5. On cubic multisections of Eisenstein series, (with student A. Alaniz),
    The Ramanujan Journal, Volume 35, Issue 3, pp 391-403, 2014.

  6. A theory of theta functions to the quintic base,
    Journal of Number Theory, Volume 134, pp. 49-92, 2014.

  7. Parameterizations for quintic Eisenstein series, (with students R. Charles and A. Mendoza),
    Journal of Number Theory, Volume 133, Number 1, pp. 195-214, 2013.

  8. 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.

  9. Differential equations for cubic theta functions,
    International Journal of Number Theory, Volume 7, Number 6, pp. 1-12, 2011.

  10. Zeros of generalized Rogers-Ramanujan series: Asymptotic and combinatorial properties,
    Journal of Approximation Theory, Volume 162, Issue 5, pp. 910-930, 2010.

  11. Combinatorics of Generalized q-Euler Numbers, (with A. J. Yee),
    Journal of Combinatorial Theory, Series A, Volume 117, Issue 4, pp. 361-388, 2010.

  12. Coupled systems of differential equations for modular forms of level n,
    Ramanujan Rediscovered, Ramanujan Mathematical Society, Lecture Note Series, 2010.

  13. Basic representations for Eisenstein series from their differential equations,
    Journal of Mathematical Analysis and Applications, Volume 350, Issue 1, pp. 135-146, 2009.

  14. Hadamard products for generalized Rogers-Ramanujan series,
    Journal of Approximation Theory, Volume 151, Number 2, pp.~126--154, 2008.

  15. 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.

  16. 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.

  17. 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

  1. Congruences for septic theta functions,
    Not yet Submitted.

  2. Symmetric Septic Forms for Eisenstein Series, (with student E. Melendez),
    Not yet Submitted.

  3. Generators for Eisenstein series of level eleven,
    Not yet Submitted.