He is known for his asymptotic results in Bieberbach conjecture in 1955,[9] and for Hayman's alternatives in Nevanlinna Theory. His work with Wolfgang Fuchs gave a solution to an inverse problem of the Nevanlinna theory for entire functions, predating David Drasin's 1976 work.
Hayman, Walter K. (1993), "A problem on Fourier series arising from an Isoperimetric inequality", in Ricci, Paolo Emilio (ed.), Problemi attuali dell'analisi e della fisica matematica. Atti del simposio internazionale dedicato a Gaetano Fichera nel suo 70o compleanno. Taormina, 15–17 ottobre 1992, Roma: Dipartimento di Matematica Università di Roma La Sapienza – Aracne Editrice, pp.119–125, MR1249093, Zbl0851.42009.
Hayman, W. K. (2014), My Life and Functions, Logic Press, pp.iv+138, ISBN978-1-326-03020-9
Hayman, W. K.; Lingham, E. F. (2019), Research Problems in Function Theory - Fiftieth Anniversary Edition, Problem Books in Mathematics, Springer, pp.VIII+284, ISBN978-3-030-25164-2
Accademia Nazionale dei Lincei (2012), Annuario dell'Accademia Nazionale dei Lincei 2012 – CDX dalla Sua Fondazione(PDF) (in Italian), Roma: Accademia Nazionale dei Lincei, p.734, archived from the original(PDF) on 4 March 2016, retrieved 6 December 2014. The "Yearbook" of the renowned Italian scientific institution, including an historical sketch of its history, the list of all past and present members as well as a wealth of information about its academic and scientific activities.