​Research Preprints

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• W. Craig, M. L. Dawsey, G.-N. Han. Inequalities and asymptotics for hook numbers in restricted partitions. (arxiv)

• K. Bringmann, W. Craig, J. Males. Asymptotics for d-fold partition diamonds and related infinite products. (arxiv)

• W. Craig, M. L. Dawsey, G.-N. Han. Properties of Hook Numbers in Restricted Classes. Submitted to Proceedings of the 36th International Conference on Formal Power Series and Algebraic Combinatorics. Extended abstract.

• W. Craig, W. Raji. The Riemann Hypothesis for period polynomials of cusp forms. Submitted for publication. (arxiv)

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Research Publications

2024

• G. Cesana, W. Craig, J. Males. Asymptotic equidistribution for partition statistics and topological invariants. Journal of Number Theory 256, 373-396 (2024). (Published version) (arxiv)

2023​​

• C. Ballantine, H. Burson, W. Craig, A. Folsom, and B. Wen. Hook length biases and general linear partition inequalities. Research in the Mathematical Sciences 10, 41 (2023). (Published version) (arxiv)

• W. Craig. Seaweed algebras and the index statistic for partitions. Journal of Mathematical Analysis and Applications 528, 2 (2023). (Published version) (arxiv)

• J. Balakrishnan, W. Craig, K. Ono, W-L. Tsai. Variants of Lehmer's speculation for newforms. Advances in Mathematics, 428, 1 (2023). (Published version) (arxiv) (Corrigendum)

2022

• ​W. Craig. On the distribution of parts into congruence classes in partitions with distinct parts. Research in Number Theory, 8, 52 (2022). (Published version) (arxiv)

• K. Bringmann, W. Craig, J. Males, K. Ono. Distributions on partitions arising from Hilbert schemes and hook lengths. Forum of Mathematics, Sigma, 10, E49 (2022). (Published version) (arxiv)

• W. Craig, M. Merca. On Ramanujan-type congruences for multiplicative functions. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 128 (2022). (Published version) (arxiv)

• J. Balakrishnan, W. Craig, K. Ono. Variations of Lehmer's conjecture for Ramanujan's tau-function. Journal of Number Theory (JNT Prime and Special Issue on Modular forms and Function Fields), 237, 3-14 (2022). (Published Version) (arxiv)

• ​W. Craig, P. Linnell. Unique product groups and congruence subgroups. Journal of Algebra and Its Applications, 21, 2 (2022). (Published Version) (arxiv)

2021​

• W. Craig, A. Pun. Distribution properties for t-hooks in partitions. Annals of Combinatorics, 25, 677-697 (2021). (Published Version) (arxiv)

• W. Craig, A. Pun. A note on the higher order Turán inequalities for k-regular partitions. Research in Number Theory, 7, 1 (2021). (Published Version) (arxiv)

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In Progress

• K. Bringmann, W. Craig, C. Nazaroglu. In progress.

• W. Bridges, W. Craig. In progress.

• W. Bridges, W. Craig, L. Rolen. In progress.

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Notes and Conference Proceedings

• W. Bridges, W. Craig. On the distribution of the norm of partitions. Submitted to Proceedings of 100 Years of Mock Theta Functions. (arxiv)

• C. Ballantine, H. Burson, W. Craig, A. Folsom, and B. Wen. On the Number of Hooks of Fixed Length in Odd versus Distinct Partitions. Seminaire Lotharingien de Combinatoire 89B, Proceedings of the 35th International Conference on Formal Power Series and Algebraic Combinatorics, 12 pp. (2023). (preprint)​

• W. Craig, A. Pun. Higher order Turán inequalities for k-regular partitions. Seminaire Lotharingien de Combinatoire 84B, Proceedings of the 32th International Conference on Formal Power Series and Algebraic Combinatorics, 8 pp. (2020). (preprint)

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Ph.D. Thesis

• W. Craig. On the coefficients of q-series and modular forms. (arxiv)