Related papers: Ikeda type construction of cusp forms

In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In the local aspect, we show the $\Hom$-space is always of one…

The paper establishes an equivalence between directed homotopy categories of (diagrams of) cubical sets and (diagrams of) directed topological spaces. This equivalence both lifts and extends an equivalence between classical homotopy…

We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved…

The aim of this paper is to construct horizontal Chern forms of a holomorphic vector bundle using complex Finsler structures. Also, some properties of these forms are studied.

We realize every closed flat 3-manifold as a cusp section of a complete, finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps. Moreover, for every such 3-manifold, a dense subset of its flat metrics…

We present a construction for the holomorph of an inverse semigroup, derived from the cartesian closed structure of the category of ordered groupoids. We compare the holomorph with the monoid of mappings that preserve the ternary heap…

This work investigates flexible Kokotsakis polyhedra with a quadrangular base of equimodular elliptic type, filling a significant gap in the literature by providing the first explicit constructions of this type together with an explicit…

In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex…

We extend the Kuga-Satake construction to the case of limit mixed Hodge structures of K3 type. We use this to study the geometry and Hodge theory of degenerations of Kuga-Satake abelian varieties, associated to polarized variations of K3…

This note will discuss the dynamics of iterated cubic maps from the real or complex line to itself, and will describe the geography of the parameter space for such maps. It is a rough survey with few precise statements or proofs, and…

The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's…

We use the self-similar tilings constructed by the second author in "Canonical self-affine tilings by iterated function systems" to define a generating function for the geometry of a self-similar set in Euclidean space. This tubular zeta…

We introduce the zeta function of the prehomogenous vector space of binary cubic forms, twisted by the real analytic Eisenstein series. We prove the meromorphic continuation of this zeta function and identify its poles and their residues.…

In a recent paper Garoufalidis and Reid constructed pairs of 1-cusped hyperbolic 3-manifolds which are isospectral but not isometric. In this paper we extend this work to the multi-cusped setting by constructing isospectral but not…

This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are symmetric about three geodesic segments and we call those zeros that lie on these segments, real. Our…

We study a notion of cusp forms for the symmetric spaces G/H with G = SL(n,R) and H = S(GL(n-1,R) x GL(1,R)). We classify all minimal parabolic subgroups of G for which the associated cuspidal integrals are convergent and discuss the…

We study the geometry, Hodge theory and derived category of cubic fourfolds containing several planes and their associated twisted K3 surfaces. We focus on the case of two planes intersecting along a line.

We prove effective forms of the Sato-Tate conjecture for holomorphic cuspidal newforms which improve on the author's previous work (solo and joint with Lemke Oliver). We also prove an effective form of the joint Sato-Tate distribution for…

We show that certain families of iso-length spectral hyperbolic surfaces obtained via the Sunada construction are not generally simple iso-length spectral.

It is known that there is an one-to-one correspondence among the space of cusp forms, the space of homogeneous period polynomials and the space of Dedekind symbols with polynomial reciprocity laws. We add one more space, the space of…