Related papers: A Monomial Basis for the Holomorphic Functions on …
Planar functions over finite fields give rise to finite projective planes and other combinatorial objects. They exist only in odd characteristic, but recently Zhou introduced an even characteristic analogue which has similar applications.…
We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over…
The monodromy map for a rank-two system of differential equations with three Fuchsian singularities is classically solved by the Kummer formul\ae\ for Gauss' hypergeometric functions. We define the tau-function of such a system as the…
In this paper we apply a homologous version of the Cauchy integral formula for octonionic monogenic functions to introduce for this class of functions the notion of multiplicity of zeroes and $a$-points in the sense of the topological…
A standard technique for producing monogenic functions is to apply the adjoint quaternionic Fueter operator to harmonic functions. We will show that this technique does not give a complete system in L2 of a solid torus, where toroidal…
We solved the long-standing problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomial-divisor mirror map is generalized to a map between the whole Picard group and the…
We construct a Schauder basis for the space $Hol(\mathbb D)$, the space of holomorphic functions on the closed unit disk, consisting entirely of finite Blaschke products. The expansion coefficients are given explicitly. Our result remains…
A general method to construct basis functions for fermionic systems which account for the $SU(2)$ symmetry and for the translational invariance of the Hamiltonian is presented. The method does not depend on the dimensionality of the system…
The space of solutions of the rational Calogero-Moser hierarchy, and the space of solutions of the KP hierarchy whose tau functions are monic polynomials in $t_1$ with coefficients depending on $t_n$, $n > 1$, are identified, generalizing…
The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
The dependence of torsion functors on their supporting ideals is investigated, especially in the case of monomial ideals of certain subrings of polynomial algebras over not necessarily Noetherian rings. As an application it is shown how…
It gives a class of $p$-Borel principal ideals of a polynomial algebra over a field $K$ for which the graded Betti numbers do not depend on the characteristic of $K$ and the Koszul homology modules have monomial cyclic basis. Also it shows…
Suppose that $f: Y\to X$ is a proper, dominant, tamely ramified morphism of algebraic surfaces, over a perfect field. We show that it is possible to perform sequences of monoidal transforms $Y'\to Y$ and $X'\to X$ to obtain an induced…
In this paper, we prove the following result advocating the importance of monomial quadratic relations between holomorphic CM periods. For any simple CM abelian variety $A$, we can construct a CM abelian variety $B$ such that all…
We use holomorphic factorization to find the partition functions of an abelian two-form chiral gauge-field on a flat six-torus. We prove that exactly one of these partition functions is modular invariant. It turns out to be the one that…
We extend a T-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of…
We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z_M. Our primary focus is the dependence of Z_M on the geometry of M, as well as background…
In this note, we continue to highlight some applications of Theorem 1 of [3]. Here is a sample: Let $X$ be an open set in ${\bf C}^n$, $\Omega$ an open convex set in ${\bf C}$ and $f, g : X\to {\bf C}$ two holomorphic functions such that…
In this paper, we use a regularized theta lifting to construct harmonic Maass forms corresponding to binary theta functions of weight $k \ge 2$ under the $\xi$-operator. As a result, we show that their holomorphic parts have algebraic…
Topological periodic cyclic homology (i.e., $\mathbb{T}$-Tate fixed points of $THH$) has the structure of a strong symmetric monoidal functor of smooth and proper dg categories over a perfect field of finite characteristic.