Related papers: $p$-Adic $\lambda$ Functions for Cyclic Mumford Cu…
The analytic structure of elementary correlation functions of a quantum field is relevant for the calculation of masses of bound states and their time-like properties in general. In quantum chromodynamics, the calculation of correlation…
We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of…
A {\em cyclic graph} is a graph with at each vertex a cyclic order of the edges incident with it specified. We characterize which real-valued functions on the collection of cubic cyclic graphs are partition functions of a real vertex model…
A multidimensional basis of p-adic wavelets is constructed. The relation of the constructed basis to a system of coherent states (i.e. orbit of action) for some $p$-adic group of linear transformations is discussed. We show that the set of…
Let F be a number field, p a prime number. We construct the (multi-variable) p-adic L-function of an automorphic representation of $GL_2(A_F)$ (with certain conditions at places above p and $\infty$), which interpolates the complex…
Using an explicit version of the Mumford isomorphism on the moduli space of hyperelliptic curves we derive a closed formula for the Arakelov-Green function of a hyperelliptic Riemann surface evaluated at its Weierstrass points.
In this paper we give an algorithm to calculate the coefficients of the p-adic expansion of a rational numbers, and we give a method to decide whether this expansion is periodic or ultimately periodic.
The Chabauty--Kim method was developed with the aim of approaching effective Faltings', the problem of explicitly determining the finite set of rational points on a hyperbolic curve. This method has seen success with the more particular…
We determine the gonality and the Clifford index for curves on a compact smooth toric surface. Moreover, it is shown that their gonality are computed by pencils on the ambient surface. From the geometrical view point, this means that the…
The aim of this paper is to show how zeta functions and excision in cyclic cohomology may be combined to obtain index theorems. In the first part, we obtain a local index formula for "abstract elliptic pseudodifferential operators"…
The periodic points of a morphism of good reduction for a smooth projective curve with good reduction over the p-adics form a discrete set. This is used to give an interpretation of the morphic height in terms of asymptotic properties of…
In this paper, we define, for arithmetic schemes with semistable reduction, $p$-adic objects playing the roles of Tate twists in \'etale topology, and establish their fundamental properties.
In the context of random multiplicative cascade processes, we derive analytical solutions for one- and two-point cumulants with restored translational invariance. On taking ratios of cumulants in ln epsilon, geometrical effects due to…
We study the graded geometric point of view of curvature and torsion of Q-manifolds (differential graded manifolds). In particular, we get a natural graded geometric definition of Courant algebroid curvature and torsion, which correctly…
Information Theoretic analysis of the periods of a hyperelliptic curve provides more information about the well--known but abstract relationship between the branch points and the periods. Here one constructs a canonical homology basis for a…
In this paper we study the automorphism groups of real curves admitting a regular meromorphic function $f$ of degree $p$, so called real cyclic $p$-gonal curves. When $p=2$ the automorphism groups of real hyperelliptic curves where given by…
We show that the coefficients of a power series occurring in $p$-adic Fourier theory for $\mathbf{Q}_{p^2}$ have valuations that are given by an intriguing formula.
We prove a $p$-adic version of the Integral Geometry Formula for averaging the intersection of two $p$-adic projective algebraic sets. We apply this result to give bounds on the number of points in the modulo $p^m$ reduction of a projective…
We study certain step functions whose nonnegativity is related to the integrality of sequences of ratios of factorial products. In particular, we obtain a lower bound for the mean square of such step functions which allows us to give a…
In this paper we investigate the behavior of the sigma function over the family of cyclic trigonal curves $X_s$ defined by the equation $y^3 =x(x-s)(x-b_1)(x-b_2)$ in the affine $(x,y)$ plane, for $s\in D_\varepsilon:=\{s \in \mathbb{C} |…