Related papers: Inner product formula for Yoshida lifts

In this paper, we study the inner product of states corresponding to weights of finite-dimensional highest-weight representations of classical groups. We prove that the action of the raising operators would reduce a state of hight-weight…

Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted…

The objects under investigation are the stochastic integrals with respect to free Levy processes. We define such integrals for square-integrable integrands, as well as for a certain general class of bounded integrands. Using the product…

We define and apply a method to study the non-vanishing of $p$-adic cyclotomic multiple zeta values. We prove the non-vanishing of certain cyclotomic multiple harmonic sums, and, via a formula proved in another paper, which expresses a…

We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…

We establish the optimal lower bound $\gtrsim N$ for counting the number of distinct inner products of pairs from any $N$ given vectors in $\R^2$. Essentially, we lift a related incidence structure defined by inner products in the plane to…

In this article, we discuss the equality of two inner products on a vector space. Particularly, we look at some geometric properties that are given to a vector space by an inner product namely, length and angle, and we ask under what…

We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular forms also in this setting. We also consider several operations of the two types of objects, and obtain an interesting bilinear…

We generalize Kawamata's product formula for volumes of canonical divisors to arbitrary divisors using Okounkov bodies

We prove a sufficient condition for the existence of explicit first integrals for vector fields which admit an integrating factor. This theorem recovers and extends previous results in the literature on the integrability of vector fields…

In this paper, we give an explicit determination of the non-vanishing of the theta liftings for unitary dual pairs (U(p,q), U(r,s)). Assuming the local Gan-Gross-Prasad conjecture, we determine when theta lifts of tempered representations…

We give a reduction of the irregular case for the effective non-vanishing conjecture by virtue of the Fourier-Mukai transform. As a consequence, we reprove that the effective non-vanishing conjecture holds on algebraic surfaces.

We prove a precise formula relating the Bessel period of certain automorphic forms on ${\rm GSp}_{4}(\mathbb{A}_{F})$ to a central $L$-value. This is a special case of the refined Gan--Gross--Prasad conjecture for the groups $({\rm…

Recently, the first author [1] showed that the admissible vector-valued automorphic forms lift to the admissible ones. In this article, we study the lifts for the logarithmic vector-valued automorphic forms and explicitly compute the…

We give a necessary and sufficient criterion for the existence of Borcherds products of half-integral weight associated to even lattices that split two hyperbolic planes. In particular we prove that half-integral weight Borcherds products…

In this paper, we obtain a class of irreducible Virasoro modules by taking tensor products of the irreducible Virasoro modules $\Omega(\lambda,b)$ defined in [LZ], with irreducible highest weight modules $V(\theta,h)$ or with irreducible…

In this note we prove Jensen-type inequality for certain non-convex functions. We apply our idea to prove some inequalities which were suggested at some high-level math olympiades.

In this paper it is proved that a mean-value of the product of some factors $|\zeta|^2$ is asymptotically equal to the product of the mean-values of $\zeta|^2$, and this holds true for every fixed number of the factors.

We prove that the system of Gromov-Witten invariants of the product of two varieties is equal to the tensor product of the systems of Gromov-Witten invariants of the two factors.

We prove existence results for nodal solutions of the Yamabe equation that are constant along the level sets of an isoparametric function.