Joseph Dillon

Curriculum Vitae

Below are links to a few articles I’ve been working on…

On the convexity of the square of the modulus of the zeta function in the critical strip. p 1-11. (2023).

On the oscillations of the square of the modulus of the Xi function along the real line. p 1-7. (2019).

Algorithms to locate zeros of the zeta function. p 1-5. (2017).

On the oscillations of the square of the modulus of the zeta function along the critical line. p 1-6. (2018).

Below is a link to the poster I presented at IMS2024 and a supporting article…

Symmetry and the Riemann zeta function. Poster. (2024).

Envelopes of the square of the modulus of the zeta function on the critical line. Supporting article. p 1-6. (2024).

Research Interests

Spent a decade as a theoretical chemist developing methods to model energy and charge transfer processes in molecular systems. For the past few years I’ve been investigating connections between this work and research in other areas of physics and mathematics.

Fig. 3 - Graph of |ζ|²(1/2,t) / |ζ’|²(1/2,t)[Green], 16/j(t)²[Blue] and the
difference between 16/j(t)² and 4/Log²(t/2π)[Dashed Red] where
j(t)=2 log(π)-ψ(1/4-it/2)-ψ(1/4+it/2), ψ(s) denotes the digamma
function and j(t)~-2 Log(t/2π) for sufficiently large t.

Fig. 1 - Graph of non-adiabatic potential energy function for (CH)₂N₃.

Fig. 4 - Graph of |Υ|²(t,σ)=|ζ|²(1/2-t,σ) / |ζ|²(1/2+t,σ) for 7≤σ≤100 and
|t|< 1/2. Note that (σ,t,Y)∊ℝ³ such that |Υ|²(t,σ)=1 are marked
in Red and that t=0 corresponds with the critical line.

Fig. 2 - Graph of non-adiabatic potential energy function for H₃O.