Related papers: All-order alpha'-expansion of one-loop open-string…
The Veneziano amplitude for the tree-level scattering of four tachyonic scalar of open string theory has an arithmetic analogue in terms of the p-adic gamma function. We propose a quantum extension of this amplitude using the q-extended…
In this work we study the solutions of the equation $z^pR(z^k)=\alpha$ with nonzero complex $\alpha$, integer $p,k$ and $R(z)$ generating a (possibly doubly infinite) totally positive sequence. It is shown that the zeros of…
We use the notion of Milnor fibres of the germ of a meromorphic function and the method of partial resolutions for a study of topology of a polynomial map at infinity (mainly for calculation of the zeta-function of a monodromy). It gives…
A systematic formulation of the higher genus expansion in topological string theory is considered. We also develop a simple way of evaluating genus zero correlation functions. At higher genera we derive some interesting formulas for the…
The string corrections of tree-level open-string amplitudes can be described by Selberg integrals satisfying a Knizhnik-Zamolodchikov (KZ) equation. This allows for a recursion of the $\alpha'$-expansion of tree-level string corrections in…
In this paper, we explicitly obtain inhomogeneous Picard-Fuchs equations for Abelian integrals $I_{i,j}^+(h)$, where $I_{i,j}^+(h)$ is an integral along orbital arcs defined by polynomials $\frac{1}{2}y^2 + F(x)=h$. Moreover, we discuss the…
We study factorizations of topological string amplitudes on higher genus Riemann surfaces with multiple boundary components and find quantum A-infinity relations, which are the higher genus analog of the (classical) A-infinity relations on…
We use the remodeling approach to the B-model topological string in terms of recursion relations to study open string amplitudes at orbifold points. To this end, we clarify modular properties of the open amplitudes and rewrite them in a…
New monodromy relations of loop amplitudes are derived in open string theory. We particularly study N-point one-loop amplitudes described by a world-sheet cylinder (planar and non-planar) and derive a set of relations between subamplitudes…
This study introduces $(\alpha,a)$-parameterized Hurwitz-Lerch type poly-Bernoulli and poly-Cauchy numbers and polynomials, extending classical sequences through the Hurwitz-Lerch zeta function. We derive generating functions, recurrences,…
We extend topological string methods in order to perform WKB approximations for quantum mechanical problems with higher order potentials efficiently. This requires techniques for the evaluation of the relevant quantum periods for Riemann…
In this note, by using the result in one variable, we obtain asymptotic expansions of oscillatory integrals for certain multivariable phase functions with {\bf degenerate} singular points. Moreover by using this result, we have asymptotic…
By using the Wilf-Zeilberger method, we prove a novel finite combinatorial identity related to a bivariate generating function for $\zeta(2+r+2s)$ (an extension of a Bailey-Borwein-Bradley Apery-like formula for even zeta values). Such…
I describe a method for determining the coefficients of scalar integrals for one-loop amplitudes in quantum field theory. The method is based upon generalized unitarity and the behavior of amplitudes when the free parameters of the cut…
In the present article, we introduce beta-expansions in the ring $\mathbb{Z}_p$ of $p$-adic integers. We characterise the sets of numbers with eventually periodic and finite expansions.
We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental…
We give a complete classification and present new exotic phenomena of the meromorphic structure of $\zeta$-functions associated to general self-adjoint extensions of Laplace-type operators over conic manifolds. We show that the meromorphic…
In \cite{[NE]} we introduce $\alpha$-expansions a real numbers in $(0,1]$, given by \[ \sum_{i=1}^{\infty}(\alpha-1)^{i-1}\alpha^{-(d_{1}+\dots+d_{i})}\] with $\alpha>1$ and $d_{i}\in\mathbb{N}$ and discuss ergodic theoretical and dimension…
The question of constructing the finite genus quasiperiodic solutions for the Ablowitz-Ladik hierarchy (ALH) is considered by establishing relations between the ALH and the Fay's identity for the theta-functions. It is shown that using a…
In this contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions…