Related papers: Theta blocks related to root systems

In a series of papers we have been studying the geometric theta correspondence for non-compact arithmetic quotients of symmetric spaces associated to orthogonal groups. It is our overall goal to develop a general theory of geometric theta…

Chinta, Jorgenson and Karlsson introduced a generalized version of the determinant formula for the Ihara zeta function associated to finite or infinite regular graphs. On the other hand, Konno and Sato obtained a formula of the…

We obtain a vector-valued subordination principle for $(g_{\alpha}, g_{\alpha})$-regularized resolvent families which unified and improves various previous results in the literature. As a consequence we establish new relations between…

While studying some properties of linear operators in a Euclidean Jordan algebra, Gowda, Sznajder and Tao have introduced generalized lattice operations based on the projection onto the cone of squares. In two recent papers of the authors…

Jacobi theta functions with rational characteristics can be viewed as vector-valued Jacobi forms. Theta relations usually correspond to different constructions of certain Jacobi forms. From this observation, we extract a new approach, which…

In this paper, we consider the decomposition of theta series for lattice cosets of ternary lattices. We show that the natural decomposition into an Eisenstein series, a unary theta function, and a cuspidal form which is orthogonal to unary…

We study a set of topological roots of the local Bernstein-Sato polynomial of arbitrary plane curve singularities. These roots are characterized in terms of certain divisorial valuations and the numerical data of the minimal log resolution.…

t is proved in this paper that there is a fine correlation between the values of $|\zeta(1/2+i\varphi(t)/2)|^4$ and $|\zeta(1/2+it)|^2$ which correspond to two segments with gigantic distance each from other. This new asymptotic formula…

We study the intersection theory of the $\Theta^{r,s}$-classes, where $r \geq 2$ and $1 \le s \le r-1$, which are cohomological field theories obtained as the top degrees of Chiodo classes. We show that the recently introduced generalized…

We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric…

We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki's…

We study the Coh zeta function for a family of inert quadratic orders, which we conjecture to be given by $t$-deformed Bressoud $q$-series. This completes a trilogy connecting the zeta functions of ramified and split quadratic orders to the…

In $2003$, Pei and Wang introduced higher level analogs of the classical Cohen--Eisenstein series. In recent joint work with Beckwith, we found a weight $\frac{1}{2}$ sesquiharmonic preimage of their weight $\frac{3}{2}$ Eisenstein series…

Let $R$ be a root system of type BC in $\mathfrak a=\mathbb R^r$ of general positive multiplicity. We introduce certain canonical weight function on $\mathbb R^r$ which in the case of symmetric domains corresponds to the integral kernel of…

We prove a seesaw identity for theta functions with polynomials, and establish a formula for the corresponding theta contractions. We then use it to determine the restrictions of theta lifts to sub-Grassmannians, with some applications.

We prove certain general forms of functional relations among Witten multiple zeta-functions in several variables (or zeta-functions of root systems). The structural background of those functional relations is given by the symmetry with…

In this paper, we present an explicit formula that connects the Kontsevich-Witten tau-function and the Hodge tau-function by differential operators belonging to the $\hat{GL(\infty)}$ group. Indeed, we show that the two tau-functions can be…

We find the Hecke-Rogers type series representations of generating functions of the Hurwitz class numbers which is very close to certain mock theta functions. We also prove two combinatorial interpretation of Hurwitz class numbers appeared…

We study the zeros of theta functions $\Theta_{\Gamma_{4k}}$ associated with the lattices $\Gamma_{4k}$, a family of self-dual lattices generalizing the $\mathsf{E}_{8}$ lattice. Our results show two different behaviors of the zeros…

In this paper we use automorph class theory formalism to construct a lifting of similitudes of quadratic Z-modules of arbitrary ternary nondegenerate quadratic forms to morphisms between certain subrings of associated Clifford algebras. The…