Related papers: Efficient computation of BSD invariants in genus 2
An invariant of a model of genus one curve is a polynomial in the coefficients of the model that is stable under certain linear transformations. The classical example of an invariant is the discriminant, which characterizes the singularity…
S.-W. Zhang recently introduced a new adelic invariant for curves of genus at least 2 over number fields and function fields. We calculate this invariant when the genus is equal to 2.
In this present manuscript, we discuss properties of modified Baskakov-Durrmeyer-Stancu (BDS) operators with parameter $\gamma>0$. We compute the moments of these modified operators. Also, establish point-wise convergence, Voronovskaja type…
High-dimensional planted problems, such as finding a hidden dense subgraph within a random graph, often exhibit a gap between statistical and computational feasibility. While recovering the hidden structure may be statistically possible, it…
Invariance of Type IIB superstring theory under SL(2,Z) or S-duality implies dependence on the complex coupling T through real and complex modular forms in T. Their structure may be understood explicitly in an expansion of superstring…
We present an algorithm to compute values L(s) and derivatives of L-functions of motivic origin numerically to required accuracy. Specifically, the method applies to any L-series whose Gamma-factor is a product of any number of…
We define the BPS invariants of Gopakumar-Vafa in the case of irreducible curve classes on Calabi-Yau 3-folds. The main tools are the theory of stable pairs in the derived category and Behrend's constructible function approach to the…
We propose an algorithm for computing bases and dimensions of spaces of invariants of Weil representations of $\mathrm{SL}_2(\mathbb{Z})$ associated to finite quadratic modules. We prove that these spaces are defined over $\mathbb{Z}$, and…
We present a system that enables rapid model experimentation for tera-scale machine learning with trillions of non-zero features, billions of training examples, and millions of parameters. Our contribution to the literature is a new method…
We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamiltonian systems. The manipulations required involve complex…
It is well-established that the dimensional reduction of the classical effective action of string theory at any order of $\alpha'$ on a circle of arbitrary radius remains invariant under the higher-derivative extension of Buscher…
We introduce a notion of integration on the category of proper birational maps to a given variety $X$, with value in an associated Chow group. Applications include new birational invariants; comparison results for Chern classes and numbers…
Modular invariants of families of curves are Arakelov invariants in arithmetic algebraic geometry. All the known uniform lower bounds of these invariants are not sharp. In this paper, we aim to give explicit lower bounds of modular…
Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case…
We calculate O(alpha_s) two-loop virtual corrections to the differential decay width dGamma(B --> X_s l^+ l^-)/ds, where s is the invariant mass squared of the lepton pair. We also include those contributions from gluon bremsstrahlung which…
Previous work established a connection between the geometric invariant theory of the third exterior power of a 9-dimensional complex vector space and the moduli space of genus 2 curves with some additional data. We generalize this…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
We write the relations that characterize the simpliest timed automaton, the inertial delay buffer, in two versions: the non-deterministic and the deterministic one, by making use of the derivatives of the R->{0,1} functions.
We study the class numbers of integral binary cubic forms. For each $SL_2(Z)$ invariant lattice $L$, Shintani introduced Dirichlet series whose coefficients are the class numbers of binary cubic forms in $L$. We classify the invariant…
We describe an algorithm to compute the number of points over finite fields on a broad class of modular curves: we consider quotients $X_H/W$ for $H$ a subgroup of $\GL_2(\mathbb Z/n\mathbb Z)$ such that for each prime $p$ dividing $n$, the…