Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Difference of modular functions and their CM value factorization   In this paper, we use Borcherds lifting and the big CM value formula of
Bruinier, Kudla, and Yang to give an explicit factorization formula for the
norm of $\Psi(\frac{d_1+\sqrt{d_1}}2) -\Psi(\frac{d_2+\sqrt{d_2}}2)$, where
$\Psi$ is the $j$-invariant or the Weber invariant $\omega_2$. The
$j$-invariant case gives another proof of the well-known Gross-Zagier
factorization formula of singular moduli, while the Weber invariant case gives
a proof of the Yui-Zagier conjecture for $\omega_2$. The method used here could
be extended to deal with other modular functions on a genus zero modular curve.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat