MathOverflow

Let $f_i$ be a smooth function, non-negative, supported on $[Y_i, 2 Y_i]$.Let $X \ll Y_1 \cdots Y_s \ll X$.Let$$S = \sum_{X \leq x \leq 2 X} \left| \sum_{n_1 \cdots n_s = x +1 } f_1(n_1) ... f_s(n_s) - \sum_{n_1 \cdots n_s = x } f_1(n_1) ... f_s(n_s...

If we substitute this number (or any similar one), then the sum will grow infinitely, which will never lead to 1. I have a fairly superficial knowledge of mathematics, so I'm waiting for answers.

Let $H$ be a finite-dimensional semisimple Hopf algebra over $\mathbb{C}$, and let $\lambda \in H^*$ be a nonzero integral. By [LS69, §2], $\lambda$ is nondegenerate (i.e., the bilinear form $(x,y)\mapsto \lambda(xy)$ is nondegenerate).
Since $H$ is a finite-dimensional semisimple algebra over $\mathbb{C}$, it admits a $C^*$-algebra structure, although it is not known in general whether this structure can be chosen so that $H$ becomes a $C^*$-Hopf algebra....

Background:
Conformal field theories (CFTs) in two dimensions are partially characterized by a so-called central charge (characterizing the central extension of the Virasoro algebra which defines it). Under a condition of unitarity and minimality, all CFTs with...