Related papers: On p-Adic Sector of Adelic String
This article introduces a new kind of number systems on $p$-adic integers which is inspired by the well-known $3n+1$ conjecture of Lothar Collatz. A $p$-adic system is a piecewise function on $\mathbb{Z}_p$ which has branches for all…
We relate non-critical special values $p$-adic $L$-functions associated to algebraic Hecke characters of an imaginary quadratic number field with class number one to $p$-adic Coleman function called the $p$-adic Eisenstein-Kronecker series,…
After a brief review of p-adic numbers, adeles and their functions, we consider real, p-adic and adelic superalgebras, superspaces and superanalyses. A concrete illustration is given by means of the Grassmann algebra generated by two…
Closed string field theory leads to a generalization of Lie algebra which arose naturally within mathematics in the study of deformations of algebraic structures. It also appeared in work on higher spin particles \cite{BBvD}. Representation…
The Fourier coefficients of the Siegel-Eisenstein series are p-adically continued for all primes p, as meromorphic functions, using the reciprocal of a product of L-functions. A construction of p-adic meromorphic families of such series is…
After recalling standard nonlinear port-Hamiltonian systems and their algebraic constraint equations, called here Dirac algebraic constraints, an extended class of port-Hamiltonian systems is introduced. This is based on replacing the…
Considering the L-function of exponential sums associated to a polynomial over a finite field F_q, Deligne proved that a reciprocal root's p-adic order is a rational number in the interval [0, 1]. Based on hypergeometric theory, in this…
We consider the couplings of RR fields with open string sector for $Dp$-${\overline{Dp}}$ backgrounds of various $p$. Proposed approach, based on the approximation of the open string algebra by the algebra of differential operators,…
Scattering amplitudes for discrete states in 2D string theory are considered. Pole divergences of tree-level amplitudes are extracted and residues are interpreted as renormalized amplitudes for discrete states. An effective Lagrangian…
We discuss a precise relation between the Veneziano amplitude of string theory, rewritten in terms of ratios of the Riemann zeta function, and two elementary criteria for the Riemann hypothesis formulated in terms of integrals of the…
We develop a theory of $p$-adic N\'eron functions on abelian varieties, depending on various auxiliary choices, and show that the global $p$-adic height functions constructed by Mazur and Tate can be decomposed into a sum of $p$-adic…
The Dedekind zeta function of a quadratic number field factors as a product of the Riemann zeta function and the $L$-function of a quadratic Dirichlet character. We categorify this formula using objective linear algebra in the abstract…
This thesis aims to study nonlocal Lagrangians with a finite and an infinite number of degrees of freedom. We obtain an extension of Noether's theorem and Noether's identities for such Lagrangians. We then set up a Hamiltonian formalism for…
Open strings on a D$p$-brane in the pp-wave spacetime, accompanied by a linear dilaton background, will be studied. Various properties of this system such as solvability of equations of motion and quantization will be investigated.
We present two types of relativistic Lagrangians for the Lorentz-Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends…
We introduce the p-adic analogue of Arakelov intersection theory on arithmetic surfaces. The intersection pairing in an extension of the p-adic height pairing for divisors of degree 0 in the form described by Coleman and Gross. It also uses…
String theory on D-brane backgrounds is open-closed string theory. Given the relevance of this fact, we give details and elaborate upon our earlier construction of oriented open-closed string field theory. In order to incorporate explicitly…
The role of torsion and a scalar field $\phi$ in gravitation in the background of a particular class of the Riemann-Cartan geometry is considered here. Some times ago, a Lagrangian density with Lagrange multipliers has been proposed by the…
We study the spectrum of the operator $D^*D$, where the operator $D$, introduced in \cite{KMR}, is a forward derivative on the $p$-adic tree, a weighted rooted tree associated to $\mathbb Z_p$ via Michon's correspondence. We show that the…
The aim of this paper is to prove conjectures concerning $p$-adic valuations of Stirling numbers of the second kind $S(n,k)$, $n,k\in\mathbb{N}_+$, stated by Amdeberhan, Manna and Moll and Berrizbeitia et al., where $p$ is a prime number.…