We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$‎. ‎This representation is obtained from the residues of Eisenstein series on this group‎. ‎If $r$ is odd‎, ‎$nle r

We determine essentially completely the theta correspondence arising from the dual pair PGL3 × G2 ⊂ E6 over a p-adic field. Our first result determines the theta lift of any non-supercuspidal representation of PGL3 and shows that the lifting respects Langlands functoriality. Our second result shows that the theta lift θ(π) of a (non-self-dual) supercuspidal representation π of PGL3 is an irredu...

In our previous paper [10], we established a theta correspondence between vector-valued holomorphic Siegel modular forms and cohomology with local coefficients for local symmetric spaces attached to real orthogonal groups. This correspondence is realized via theta functions associated to explicitly constructed ”special” Schwartz forms. These forms give rise to relative Lie algebra cocycles for ...

Helton and Vinnikov proved that every hyperbolic ternary form admits a symmetric derminantal representation via Riemann theta functions. In the case the algebraic curve of the hyperbolic ternary form is elliptic, the determinantal representation of the ternary form is formulated by using Weierstrass ℘-functions in place of Riemann theta functions. An example of this approach is given.

We find identities between theta constants with rational characteristics evaluated at period matrix of R, a cyclic 3 sheeted cover of the sphere with 3k branch points λ1...λ3k. These identities follow from Thomae formula [BR]. This formula expresses powers of theta constants as polynomials in λ1...λ3k. We apply the representation of the symmetric group to find relations between the polynomials ...

Semantic modeling usuing theta-roles: a natural language processing-based approach to conceptual representation"

Encoding of behavioral episodes as spike sequences during hippocampal theta oscillations provides a neural substrate for computations on events extended across time and space. However, the mechanisms underlying the numerous and diverse experimentally observed properties of theta sequences remain poorly understood. Here we account for theta sequences using a novel model constrained by the septo-...

Encoding of behavioral episodes as spike sequences during hippocampal theta oscillations provides a neural substrate for computations on events extended across time and space. However, the mechanisms underlying the numerous and diverse experimentally observed properties of theta sequences remain poorly understood. Here we account for theta sequences using a novel model constrained by the septo-...