in preparation.
R. Osburn and M. Storzer, Arborescent links and modular tails,
submitted.
R. Osburn, Knot theory and Rogers-Ramanujan type identities,
Srinivasa Ramanujan: His Life, Legacy and Mathematical Influence (Springer), accepted for publication.
S. Crew, V. Fantini, A. Goswami, R. Osburn and C. Wheeler, Resurgence, Habiro elements and strange identities,
Communications in Number Theory and Physics, 19, no. 2, (2025), 289-317.
K. Allen and R. Osburn, Unimodal sequences and mixed false theta functions,
Advances in Mathematics, 473 (2025), Paper No. 110293.
B. Alinquant and R. Osburn, On sporadic sequences,
Monatshefte für Mathematik, 205, no. 2, (2024), 217-234.
J. Lovejoy and R. Osburn, Rank deviations for overpartitions,
Research in Number Theory, 10, no. 3, (2024), Paper No. 67.
A. Goswami, A. Jha, B. Kim and R. Osburn, Asymptotics and sign patterns for coefficients in expansions of Habiro elements,
Mathematische Zeitschrift, 304, no. 4, (2023), 57.
J. Dousse and R. Osburn, A q-multisum identity arising from finite chain ring probabilities,
Electronic Journal of Combinatorics, 29, no. 2, (2022), Paper No. 2.4.
J. Lovejoy and R. Osburn, The colored Jones polynomial and Kontsevich-Zagier series for double twist knots,
Journal of Knot Theory and its Ramifications, 30, no. 5, (2021), 2150031.
A. Goswami and R. Osburn, Quantum modularity of partial theta series with periodic coefficients,
Forum Mathematicum, 33, no. 2, (2021), 451-463.
S. H. Chan, R. Mao and R. Osburn, Variations of Andrews-Beck type congruences,
Journal of Mathematical Analysis and Applications, 495, no. 2, (2021), 124771.
C. Bijaoui, H. Boden, B. Myers, R. Osburn, W. Rushworth, A. Tronsgard and S. Zhou, Generalized Fishburn numbers and torus knots,
Journal of Combinatorial Theory, Series A, 178 (2021), 105355.
D. McCarthy, R. Osburn and A. Straub, Sequences, modular forms and cellular integrals,
Mathematical Proceedings of the Cambridge Philosophical Society, 168, no. 2, (2020), 379-404.
J. Lovejoy and R. Osburn, The colored Jones polynomial and Kontsevich-Zagier series for double twist knots, II,
New York Journal of Mathematics, 25 (2019), 1312-1349.
R. Osburn and A. Straub, Interpolated sequences and critical L-values of modular forms,
Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, 327-349, Texts & Monographs in Symbolic Computation, Springer, 2019.
F. Luca, P. Moree, R. Osburn, S. Saad Eddin and A. Sedunova, Constrained ternary integers,
International Journal of Number Theory, 15, no. 2, (2019), 407-431.
R. Osburn, A. Straub and W. Zudilin, A modular supercongruence for 6F5 : an Apéry-like story,
Annales de l'Institut Fourier (Grenoble), 68, no. 5, (2018), 1987-2004.
J. Lovejoy and R. Osburn, Mock theta double sums,
Glasgow Mathematical Journal, 59, no. 2, (2017), 323-348.
P. Beirne and R. Osburn, q-series and tails of colored Jones polynomials,
Indagationes Mathematicae, 28, no. 1, (2017), 247-260.
L. Long, R. Osburn and H. Swisher, On a conjecture of Kimoto and Wakayama,
Proceedings of the American Mathematical Society, 144, no. 10, (2016), 4319-4327.
G. E. Andrews, S. H. Chan, B. Kim and R. Osburn, The first positive rank and crank moments for overpartitions,
Annals of Combinatorics, 20, no. 2, (2016), 193-207.
R. Osburn, B. Sahu and A. Straub, Supercongruences for sporadic sequences,
Proceedings of the Edinburgh Mathematical Society (2), 59, no. 2, (2016), 503-518.
A. Keilthy and R. Osburn, Rogers-Ramanujan type identities for alternating knots,
Journal of Number Theory, 161, (2016), 255-280.
R. Osburn and W. Zudilin, On the (K.2) supercongruence of Van Hamme,
Journal of Mathematical Analysis and Applications, 433, no. 1, (2016), 706-711.
S. H. Chan, R. Mao and R. Osburn, On recursions for coefficients of mock theta functions,
Research in Number Theory, 1:29 (2015).
J. Lovejoy and R. Osburn, Real quadratic double sums,
Indagationes Mathematicae, 26, no. 4, (2015), 697-712.
J. Lovejoy and R. Osburn, On two 10th order mock theta identities,
The Ramanujan Journal, 36, no. 1-2, (2015), 117-121.
R. Osburn, q-hypergeometric series, alternating knots and identities,
Oberwolfach Reports, 11, no. 3, (2014), 2164-2167.
J. Lovejoy and R. Osburn, Mixed mock modular q-series,
Journal of the Indian Mathematical Society, New Series. Special volume to commemorate the 125th birth anniversary of Srinivasa Ramanujan, (2013), 45-61.
J. Lovejoy and R. Osburn, q-hypergeometric double sums as mock theta functions,
Pacific Journal of Mathematics, 264, no. 1, (2013), 151-162.
R. Osburn and B. Sahu, A supercongruence for generalized Domb numbers,
Functiones et Approximatio Commentarii Mathematici, 48, no. 1, (2013), 29-36.
J. Lovejoy and R. Osburn, The Bailey chain and mock theta functions,
Advances in Mathematics, 238 (2013), 442-458.
D. Brink, P. Moree and R. Osburn, Principal forms X^2 + nY^2 representing many integers,
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 81, no. 2, (2011), 129-139.
R. Osburn and B. Sahu, Supercongruences for Apéry-like numbers,
Advances in Applied Mathematics, 47, no. 3, (2011), 631-638.
R. Osburn and B. Sahu, Congruences via modular forms,
Proceedings of the American Mathematical Society, 139, no. 7, (2011), 2375-2381.
J. Lovejoy and R. Osburn, Quadratic forms and four partition functions modulo 3,
Integers, 11, no. 1, (2011), 47-53.
H. Chan, A. Kontogeorgis, C. Krattenthaler and R. Osburn, Supercongruences satisfied by coefficients of 2F1 hypergeometric series,
Annales des sciences mathématiques du Québec, 34, no. 1, (2010), 25-36.
J. Lovejoy and R. Osburn, M2-rank differences for overpartitions,
Acta Arithmetica, 144, no. 2, (2010), 193-212.
K. Bringmann, J. Lovejoy and R. Osburn, Automorphic properties of generating functions for generalized rank moments and Durfee symbols,
International Mathematics Research Notices, no. 2, (2010), 238-260.
K. Bringmann, J. Lovejoy and R. Osburn, Rank and crank moments for overpartitions,
Journal of Number Theory, 129, (2009), 1758-1772.
J. Lovejoy and R. Osburn, M2-rank differences for partitions without repeated odd parts,
Journal de Théorie des Nombres de Bordeaux, 21, no. 2, (2009), 313-334.
R. Osburn and C. Schneider, Gaussian hypergeometric series and supercongruences,
Mathematics of Computation, 78, no. 265, (2009), 275-292.
D. McCarthy and R. Osburn, A p-adic analogue of a formula of Ramanujan,
Archiv der Mathematik, 91, no. 6, (2008), 492-504.
J. Lovejoy and R. Osburn, Rank differences for overpartitions,
The Quarterly Journal of Mathematics, 59, no. 2, (2008), 257-273.
R. Osburn, Congruences for traces of singular moduli,
The Ramanujan Journal, 14, no. 3, (2007), 411-419.
R. Murty and R. Osburn, Representations of integers by certain positive definite binary quadratic forms,
The Ramanujan Journal, 14, no. 3, (2007), 351-359.
S. de Wannemacker, T. Laffey and R. Osburn, On a conjecture of Wilf,
Journal of Combinatorial Theory, Series A, 114, no. 7, (2007), 1332-1349.
P. Moree and R. Osburn, Two-dimensional lattices with few distances,
L'Enseignement Mathématique, 52, (2006), 361-380.
S. K. K. Choi, A. Kumchev and R. Osburn, On sums of three squares,
International Journal of Number Theory, 1, no. 2, (2005), 161-173.
R. Osburn, A remark on a conjecture of Borwein and Choi,
Proceedings of the American Mathematical Society, 133, no. 10, (2005), 2903-2909.
R. Osburn, Vanishing of eigenspaces and cyclotomic fields,
International Mathematics Research Notices, no. 20, (2005), 1195-1202.
R. Osburn, A note on 4-rank densities,
Canadian Mathematical Bulletin, 47, (2004), 431-438.
R. Osburn and B. Murray, Tame kernels and further 4-rank densities,
Journal of Number Theory, 98, (2003), 390-406.
R. Osburn, Densities of 4-ranks of K_2(O),
Acta Arithmetica, 102, (2002), 45-54.

R. Osburn, Densities of 4-ranks of K_2 of rings of integers,
Ph.D. thesis, LSU, 2001.