On the border of algebraic geometry and number theory, there is what is known as the "modularity conjecture" for certain algebraic varieties defined over $\mathbb{Q}$. Roughly speaking, this is the conjecture that there is a modular object whose Dirichlet series coincides with the L-series of the variety.

A little more specifically, if $X$ is a Calabi-Yau threefold defined over $\mathbb{Q}$ with $h^{2,1}(X)=0$, then one can form its L-series:

$$L(X, s) = \prod_{p-\text{prime}} \big(1-t_{3}(p)p^{-s} + p^{3-2s}\big)^{-1}.$$

(I'm lying slightly...the product excludes finitely many "bad" primes). Here, $t_{3}(p)$ are integers closely related to the number of points over the finite field $\mathbb{F}_{p}$ in $X$. The modularity conjecture is that $t_{3}(p)=a_{p}$ where $a_{p}$ are the Fourier coefficients of a weight 4 modular cusp form for congruence subgroup $\Gamma_{0}(N)$, for some $N$. For a nice summary, one can see (https://projecteuclid.org/download/pdf_1/euclid.kjm/1250517640).

I know in many areas in enumerative geometry/string theory various partition functions have non-trivial automorphic properties. Quite simply, I'm curious if there's any well-known or conjectural relationship of these L-series in string theory? Particularly, perhaps topological string theory on $X$ or something closely related?