Exact formulae for the fractional partition functions

Apostol, T.M.: Modular Functions and Dirichlet Series in Number Theory. Graduate Texts in Mathematics, 2nd edn. Springer, New York (1990)

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Chan, H.H., Wang, L.: Fractional powers of the generating function for the partition function. Acta Arithmetica 187, 59–80 (2019)

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Craven, T., Csordas, G.: Jensen polynomials and the Turán and Laguerre inequalities. Pac. J. Math. 136(2), 241–260 (1989)

DeSalvo, S., Pak, I.: Log-concavity of the partition function. Ramanujan J. 38(1), 61–73 (2015)

Griffin, M., Ono, K., Rolen, L., Zagier, D.: Jensen polynomials for the Riemann zeta function and other sequences. Proc. Natl. Acad. Sci. USA 116(23), 11103–11110 (2019)

Hardy, G.H., Ramanujan, S.: Asymptotic formulæ in combinatory analysis. Proc. Lond. Math. Soc. 2(1), 75–115 (1918)

Helfgott, H.A.: The ternary Goldbach conjecture is true. arXiv e-prints, page arXiv:1312.7748 (2013)

Keith, W.J.: Restricted $$k$$-color partitions. Ramanujan J. 40(1), 71–92 (2016)

Larson, H., Wagner, I.: Hyperbolicity of the partition Jensen polynomials. Res. Number Theory 5(2), 19 (2019)

Nicolas, J.-L.: Sur les entiers $$n$$ pour lesquels il y a beaucoup de groupes abéliens d’ordre $$n$$. Ann. Insti. Fourier 28(4), 1–16 (1978)

Olver, F.W.J., Olde Daalhuis, A.B., Lozier, D.W., Schneider, B.I., Boisvert, R.F., Clark, C.W., Miller, B.R., B.V. Saunders, (eds.) NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/, Release 1.0.23 of 2019-06-15.

Paris, R.: An Inequality for the Bessel function $${J}_{\nu }(\nu x)$$. SIAM J. Math. Anal. 15(1), 203–205 (1984)

Rademacher, H.: On the Partition Function $$p(n)$$. Proc. Lond. Math. Soc. s2–43(1), 241–254 (1938)

Watson, G.N.: A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge (1922)