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Based on Guillemin's work on gauged Lagrangian distributions, we will introduce the notion of a poly-$\log$-homogeneous distribution as an approach to $\zeta$-functions for a class of Fourier Integral Operators which includes cases of…

The concept and the construction of modular graph functions are generalized from genus-one to higher genus surfaces. The integrand of the four-graviton superstring amplitude at genus-two provides a generating function for a special class of…

For an elliptic curve $E$ defined over a field $k\subset \mathbb C$, we study iterated path integrals of logarithmic differential forms on $E^\dagger$, the universal vectorial extension of $E$. These are generalizations of the classical…

We study some Dirichlet problem for a $p$--Laplacian type operator in the setting of Orlicz--Zygmund space $L^q\log^{-\alpha}L(\Omega,\mathbb R^N)$, $q >1$ and $\alpha>0$. More precisely, our aim is to establish which assuptions on the…

We define the doubling zeta integral for smooth families of representations of classical groups. Following this we prove a rationality result for these zeta integrals and show that they satisfy a functional equation. Moreover, we show that…

We give a combinatorial expansion of a Schubert homology class in the affine Grassmannian Gr_{SL_k} into Schubert homology classes in Gr_{SL_{k+1}}. This is achieved by studying the combinatorics of a new class of partitions called…

A method for finding the exact analytical solutions for the bulk and edge energy levels and corresponding eigenstates for all commensurate Aubry-Andr\'e/Harper single-particle models under open boundary conditions is presented here, both…

We employ the slice spectral sequence, the motivic Steenrod algebra, and Voevodsky's solutions of the Milnor and Bloch-Kato conjectures to calculate the hermitian $K$-groups of rings of integers in number fields. Moreover, we relate the…

This is a sequel of our previous paper where we described an algorithm to find a solution of differential equations for master integrals in the form of an $\epsilon$-expansion series with numerical coefficients. The algorithm is based on…

We study growth and complexity of \'etale groupoids in relation to growth of their convolution algebras. As an application, we construct simple finitely generated algebras of arbitrary Gelfand-Kirillov dimension $\ge 2$ and simple finitely…

We define the twisted doubling zeta integrals of Cai-Friedberg-Ginzburg-Kaplan in the setting of algebraic families. We then prove a rationality result and a functional equation for these zeta integrals. This allows us to define an…

The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in genus 1. We find an explicit formula for any solution…

In this article we present a method to generate analytic expressions for the integral coefficients of loop amplitudes using numerical evaluations only. We use high-precision arithmetic to explore the singularity structure of the…

We suggest a simple algebraic approach to fix the elements of the $\{ \beta \}$-expansion for renormalization group invariant quantities, which uses additional degrees of freedom. The approach is discussed in detail for N$^2$LO calculations…

Let $\alpha>0$ be a constant, let $\ell\ge0$ be an integer, and let $\Gamma(z)$ denote the classical Euler gamma function. With the help of the integral representation for the Riemann zeta function $\zeta(z)$, by virtue of a monotonicity…

We consider the Schr\"odinger operator on a combinatorial graph consisting of a finite graph and a finite number of discrete half-lines, all jointed together, and compute an asymptotic expansion of its resolvent around the threshold $0$.…

We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) non-commutative p-extension of a totally real number field such that the finite part of its Galois group is a pgroup with exponent p. We first calculate…

We study the q-deformed Knizhnik-Zamolodchikov equation in path representations of the Temperley-Lieb algebras. We consider two types of open boundary conditions, and in both cases we derive factorised expressions for the solutions of the…

In this article, we establish in a rigorous mathematical way that Koba-Nielsen amplitudes defined on any local field of characteristic zero are bona fide integrals that admit meromorphic continuations in the kinematic parameters. Our…

In this paper we use automorph class theory formalism to construct a lifting of similitudes of quadratic Z-modules of arbitrary ternary nondegenerate quadratic forms to morphisms between certain subrings of associated Clifford algebras. The…