Orion Crest, Series_1

Chapter 103: Ideas emerging

　　Having a car was very convenient indeed, and after a thoroughly relaxing afternoon in Philadelphia with a day of fun and a movie later, Orion and Isabel had dinner and then left to drive back to Princeton.

　　Parking his car in the car park next to the Institute for Advanced Study, Orion, in a good mood, hummed a little tune as he walked back to the apartment building full of history and stepped on the stairs.

　　As he walked up to the first floor, a sweatshirt-clad Molina emerged from her room carrying a rubbish bag, looking like she was about to go out for a jog.

　　Taking one look at Orion, she snorted in a flirtatious tone, "Out picking up girls?"

　　"Went car shopping."

　　Waving the car keys on his index finger, Orion didn't say much to her and turned around to go back to his room.

　　After entering his single flat, he dropped his jacket and car keys on the sofa, first went to the kitchen to make himself a cup of coffee, then returned to his work desk and sat down, ready to continue the work he was halfway through in the morning.

　　Just then, a message from Cara suddenly popped up in his mobile phone screen.

　　[Master, there's a new email! OVO].

　　From Professor Frank?

　　Receiving Cara's reminder, Orion opened his computer and logged into his mailbox, only to find out that there wasn't just one, there were a total of two emails lying inside.

　　One of them was almost three days old, probably sent when he was in retreat, maybe Cara had reminded him again, but he just didn't notice it. Because the sending address was a bit unfamiliar, Orion, who was afraid of delaying something, clicked on this mail first.

　　[Dear Mr. Orion, this is Vera Puyol who greets you from Berkeley, I have some questions about the issue I discussed with you last time, and I wonder if I can take up a bit of your precious time?]

　　Puyol?

　　Although the spelling is in English, it's probably Slavic from the pronunciation.

　　However, judging from the wording of the letter, this little girl was a bit too polite, and he wasn't really a renowned professor, so there was really no need to be so formal.

　　Shaking his head, Orion put these irrelevant matters aside, and crossed over to the flattering wording and the adoration of himself between the lines, and then looked directly to the main part of the text.

　　[...... In the paper reported by Professor Helfgott at the mid-year meeting of the Federal Mathematical Society, how is it that the equation J(n) = ∫Φ(λ) · G(λ) squared ·H(λ) · e|-nλ|dλ on the third page, line 11, leads directly to the conclusion in the paper's proposition (2.1)?]

　　Seeing this, Orion's eyebrows raised slightly.

　　Yo, the perception is quite impressive.

　　As expected, IMO gold medallists do have a higher-than-average talent in maths.

　　At least compared to the conceptual question she asked herself last time about 'Contour integration' and 'Residue theorem', this question was kind of close to the core part of the Circle Method.

　　Orion smiled and edited the email to reply.

　　[Since we're going to be working with intervals for the use of the circle method and building several Uniform distribution results, we have to pave the way for our theory. So, let's write S1(q, α) = ∑e(αm cubed/q) and C1(q, α) = ∑e(αm cubed/q squared), carrying over into Td(n, q) = ∑S1(q, αd cubed) · |C1(q, αd cubed)| ·e(-an/q)/qψ squared (q) ...... Then, what we can get? Think for yourself.]