Princeton campus.
It was the coldest time of the year in New Jersey. Silvery snowflakes drifted outside the window. Snow that refused to melt piled up along the windowsills and rooftops, decorating this Oxford-style campus steeped in academia like a fairy-tale castle.
Quietly seated in the activity room of that "castle," Vera sat at her desk looking at her computer. Together with the bookshelves beside her and the snow outside, she looked like a painting.
Her pale golden hair fell softly around her. Though her fair complexion carried a sickly pallor that made people worry, the gentleness and strength shining from her sapphire-like eyes were reassuring, adding a faintly dazzling touch to her presence.
Lu Zhou's reply filled the computer screen.
Its concise style and straight-to-the-point wording were very much like him.
[I've read your email.]
[Your approach of using the theory of irreducible unitary representations of the octonionic Heisenberg Group and applying a Fourier transform to it is indeed a very interesting improvement.]
[It also reminded me of a result Levinson and Professor Montgomery jointly proved in 1974: a quantitative version of the weak form of the Riemann Hypothesis. Namely, the ratio between the number of zeros of ζ'(s) in the open region {-1＜Re(s)＜12, T1＜Im(s)＜T2} and the number of zeros of ζ(s) in {0＜Re(s)＜12, T1＜Im(s)＜T2} asymptotically approaches 1... A similar method was used there as well.]
[Very good. The idea you proposed happens to indirectly answer something I had long been doubtful about. Do you remember what I said a long time ago? The Riemann Hypothesis is a problem in Analytic Number Theory, but at its core, it remains a problem in Complex Analysis. We must approach it with methods for solving problems in Complex Analysis, but we cannot limit ourselves to that alone.]
[My suggestion is to begin