Chapter 291: Riemann Hypothesis Symposium (3)
"...In summary, it was precisely those geometric trajectories I observed at the amusement park that gave me some inspiration."
"Geometry naturally exists in our world, and mathematics itself is known as the language of the universe. Perhaps drawing inspiration from such things is not a bad approach."
Xiao Yi smiled slightly. "Consider this a small suggestion from me."
Many of the mathematicians present immediately nodded in agreement.
Although this method still sounded somewhat miraculous to them, that did not stop them from learning from Xiao Yi.
As long as it was a method recommended by Xiao Yi, they were willing to give it a try. Perhaps it would suit them.
"Now that I have explained how I came up with developing modular curves from the higher-dimensional case, let us continue discussing how I ultimately derived the Generalized Modular Curve."
"At first, I tried modular curves. It was easy to discover that although modular curves provided a geometric framework for studying extended L-functions, they could not fully explain all the properties of extended L-functions. In particular, for certain types of extended L-functions, their special values did not seem to align well with the geometry of modular curves."
"After that, I had to thank my research into Theoretical Physics for giving me some inspiration."
"We all know that physics uses certain higher-dimensional geometric spaces to study physical phenomena, such as Calabi-Yau manifolds. This gave me some inspiration."
"So, this higher-dimensional modular curve should contain ordinary modular curves as an independent case, while also containing more information to characterize extended L-functions beyond the ordinary ones."
"Now, we can give a simple definition."
"For an n-dimensional Generalized Modular Curve, denoted by X_f^(n), it is an n-dimensional complex manifold that parameterizes a special class of n-dimensional Abelian varieties. These