Related papers: Round about Theta. Part I Prehistory
The aim of this short note is to develop a (co)homology theory for topological spaces together with the specialisation preorder. A known way to construct such a (co)homology is to define a partial order on the topological space starting…
Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
This article, intended for a general mathematical audience, is an informal review of some of the many interesting links which have developed between quantum cohomology and "classical" mathematics. It is based on a talk given at the Autumn…
We describe in detail three distinct families of generalized zeta functions built over the (nontrivial) zeros of a rather general arithmetic zeta or L-function, extending the scope of two earlier works that treated the Riemann zeros only.…
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…
This is a chapter in an upcoming book on aperiodic order. We go over different versions of tiling cohomology (\v Cech, pattern-equivariant, PV, quotient) with emphasis on the inverse limit constructions used to compute these cohomologies.…
This is a survey covering aspects of varied work of the authors with Mohammed Abouzaid, Paul Hacking, and Sean Keel. While theta functions are traditionally canonical sections of ample line bundles on abelian varieties, we motivate, using…
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 his article "Transcending Classical Invariant Theory" (J.A.M.S., 1989, Vol 2), Roger Howe established a correspondence between representations of a dual pair of reductive groups. This correspondence is known as Howe's correspondence or…
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties…
This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…
Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras $\Theta.$ For every algebra $H$ in $\Theta$ one can consider algebraic geometry in $\Theta$ over $ H.$ Correspondingly, algebras in…
A functional equation between the zeta distributions can be obtained from the theory of prehomogeneous vector spaces. We show that the functional equation can be extended from the Schwartz space to certain degenerate principal series.
In our previous paper [math.NT/0408050], we established a correspondence between vector-valued holomorphic Siegel modular forms and cohomology with local coefficients for local symmetric spaces $X$ attached to real orthogonal groups of type…
This paper contains results related to synthesis and presentation of abstract automata by fragments of behaviour and investigates the structure of the classes of finite connected initial output-less automata specified by systems of defining…
The aim of this article is to illustrate, on the example of Dwork hypersurfaces, how the study of the representation of a finite group of automorphisms of a hypersurface in its etale cohomology allows to factor its zeta function.
We revisit congruence zeta functions of smooth projective varieties over finite fields in the framework of Scholze's Berkovich motives. Via this formalism and categorical traces, we construct a new zeta function, and show that it agree with…
The connection between the theory of permutation orbifolds, covering surfaces and uniformization is investigated, and the higher genus partition functions of an arbitrary permutation orbifold are expressed in terms of those of the original…