# Asymptotics: the unified transform, a new approach to the Lindelöf Hypothesis, and the ultra-relativistic limit of the Minkowskian approximation of general relativity

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Employing standard, as well as novel techniques of asymptotics, three different problems will be discussed: (i) The computation of the large time asymptotics of initial-boundary value problems via the unified transform (also known as the Fokas Method, www.wikipedia.org/wiki/Fokas_method)[1]. (ii) The evaluation of the large t-asymptotics to all orders of the Riemann zeta function [2], and the introduction of a new approach to the Lindelöf Hypothesis [3]. (iii) The proof that the ultra-relativistic limit of the Minkowskian approximation of general relativity [4] yields a force with characteristics of the strong force, including confinement and asymptotic freedom [5].

[1] J. Lenells and A. S. Fokas. The Nonlinear Schrödinger Equation with t-Periodic Data: I. Exact Results, Proc. R. Soc. A 471, 20140925 (2015).

J. Lenells and A. S. Fokas, The Nonlinear Schrödinger Equation with t-Periodic Data: II. Perturbative Results, Proc. R. Soc. A 471, 20140926 (2015).

[2] A.S. Fokas and J. Lenells, On the Asymptotics to All Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function, Mem. Amer. Math. Soc. (to appear).

[3] A.S. Fokas, A Novel Approach to the Lindelof Hypothesis, Transactions of Mathematics and its Applications (to appear).

[4] L. Blanchet and A.S. Fokas, Equations of Motion of Self-Gravitating N-Body Systems in the First Post-Minkowskian

Approximation, Phys. Rev. D 98, 084005 (2018).

[5] A.S. Fokas, Super Relativistic Gravity has Properties Associated with the Strong Force, Eur. Phys. J. C (to appear).