Related papers: Motivic zeta functions for prehomogeneous vector s…

We study the magnetic properties around the Mott transition in the Kagom\'e lattice Hubbard model by the cellular dynamical mean field theory combined with quantum Monte Carlo simulations. By investigating the q-dependence of the…

We study the space of binary cubic and quadratic forms over the ring of integers $O$ of an algebraic number field $k$. By applying the theory of prehomogeneous vector spaces founded by M. Sato and T. Shintani, we can associate the zeta…

We study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a rational point. We show this motive is contained in the thick…

We introduce a new Lie-algebraic approach to explicitly construct the motivic coaction and single-valued map of multiple polylogarithms in any number of variables. In both cases, the appearance of multiple zeta values is controlled by…

In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds…

The determination of the magnetic filed vector in solar filaments is possible by interpreting the Hanle and Zeeman effects in suitable chromospheric spectral lines like those of the He I multiplet at 10830 A. We study the vector magnetic…

In this paper we study the analytic properties of a multiple Dirichlet series associated to the prehomogeneous vector space of binary cubic forms.

We prove some results connecting the zeta functions of varieties over finite fields with the big Witt ring over $\mathbb Z$. We explore relations with motivic measures and a classical formula of Macdonald on invariants of symmetric products…

Let $G$ be a split connected semisimple group over a field. We give a conjectural formula for the motive of the stack of $G$-bundles over a curve $C$, in terms of special values of the motivic zeta function of $C$. The formula is true if…

The dynamics of modes and their states of polarizations in multimode fibers as a function of time, space, and wavelength are experimentally and theoretically investigated. The results reveal that the states of polarizations are displaced in…

We propose a computation of real motivic zeta functions for real polynomial functions, using Newton polyhedron. As a consequence we show that the weights are blow-Nash invariants of convenient weighted homogeneous polynomials in three…

We prove a recognition principle for motivic infinite P1-loop spaces over a perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of the theory of E-infinity-spaces. A framed motivic…

Some zeta functions which are naturally attached to the locally homogeneous vector bundles over compact locally symmetric spaces of rank one are investigated. We prove that such functions can be expressed in terms of entire functions whose…

For a Veech surface (x,\omega), we characterize subspaces of X^n, invariant under the diagonal action of the affine group of X. We prove that non-arithmetic Veech surfaces have only finitely many invariant subspaces of very particular shape…

We compare the topological Milnor fibration and the motivic Milnor fibre of a regular complex function with only normal crossing singularities by introducing their common extension: the complete Milnor fibration. We give two equivalent…

We show that the cellular objects in the module category over a motivic E infinity ring spectrum E can be described as the module category over a graded topological spectrum if E is strongly periodizable in our language. A similar statement…

Let X be a nonsingular algebraic variety in characteristic zero. To an effective divisor on X Kontsevich has associated a certain 'motivic integral', living in a completion of the Grothendieck ring of algebraic varieties. He used this…

In this paper we give a complete description of the Hitchin fibration on all 2-dimensional moduli spaces of rank 2 irregular Higgs bundles with two poles on the projective line. We describe the dependence of the singular fibers of the…

The Tayler instability (TI) of toroidal magnetic fields is a candidate mechanism for driving turbulence, angular momentum (AM) transport, and dynamo action in stellar radiative zones. Recently \cite{Skoutnev_2024} revisited the linear…

Let $X$ be a smooth projective curve over a field of characteristic zero and let $\mathcal D$ be an effective divisor on $X$. We calculate motivic classes of various moduli stacks of parabolic vector bundles with irregular connections on…