Related papers: Generalized Theta Series of a Lattice
We study Taylor expansions of Jacobi forms of lattice index. As the main result, we give an embedding from certain space of such forms, whether scalar-valued or vector-valued, integral-weight or half-integral-weight, of any level, with any…
In this paper, we consider the decomposition of theta series for lattice cosets of ternary lattices. We show that the natural decomposition into an Eisenstein series, a unary theta function, and a cuspidal form which is orthogonal to unary…
This paper introduces a new method for the efficient computation of oscillatory multidimensional lattice sums in geometries with boundaries. Such sums are ubiquitous in both pure and applied mathematics, and have immediate applications in…
We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $\mathbb{Z}^2$. We first prove a formula on the rotation number of a…
In a recent preprint, arXiv:1606.05495v1, Alexandrov, Banerjee, Manschot and Pioline introduced generalized error functions and used them to construct indefinite theta series associated to quadratic lattices L of signature (n-2,2). These…
We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation…
Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two…
We prove large deviation principles for the distribution of the empirical measure of the eigenvalues of Lax matrices following the Generalized Gibbs ensembles of the classical Toda chain introduced in [10]. We deduce the almost sure…
This is the first paper in a series on intrinsic Donaldson-Thomas theory, where we develop a new framework for enumerative geometry that allows the generalization of constructions and results from linear moduli stacks to general non-linear…
The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At…
General Relativity is usually formulated as a theory with gauge invariance under the diffeomorphism group, but there is a 'dilaton' formulation where it is in addition invariant under Weyl transformations, and a 'unimodular' formulation…
A novel structure-preserving algorithm for general relativity in vacuum is derived from a lattice gauge theoretic discretization of the tetradic Palatini action. The resulting model of discrete gravity is demonstrated to preserve local…
Linearised gravity has a global symmetry under which the graviton is shifted by a symmetric tensor satisfying a certain flatness condition. There is also a dual symmetry that can be associated with a global shift symmetry of the dual…
This paper is primarily concerned with generalized reduced Verma modules over $\mathbb{Z}$-graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and the coinduced modules are obtained. Moreover, the…
In this paper, we discuss the generalized Hamming weights of a class of linear codes associated with non-degenerate quadratic forms. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting…
We define generalized Hamming weights for almost affine codes. We show how various aspects and applications of generalized Hamming weights for linear codes, such as Wei duality, generalized Kung's bound, profiles, connection to wire-tap…
We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When…
A longstanding conjecture states that global symmetries should be absent in quantum gravity. By investigating large classes of Type IIB four-dimensional $\mathcal{N}=2$ effective field theories, we enlist the potential generalized global…
We explore exact generalized symmetries in the standard 2+1d lattice $\mathbb{Z}_2$ gauge theory coupled to the Ising model, and compare them with their continuum field theory counterparts. One model has a (non-anomalous) non-invertible…
In recent years, the use of machine learning has become increasingly popular in the context of lattice field theories. An essential element of such theories is represented by symmetries, whose inclusion in the neural network properties can…