Related papers: Schanuel Type Conjectures and Disjointness

We show, assuming Schanuel's conjecture, that every irreducible complex polynomial in two variables where both variables appear has infinitely many algebraically independent solutions of the form (z,e^z).

Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…

We study the Farrell-Jones Conjecture with coefficients in an additive G-category with involution. This is a variant of the L-theoretic Farrell-Jones Conjecture which originally deals with group rings with the standard involution. We show…

Let alpha = (a,b,...) be a composition. Consider the associated poset F(alpha), called a fence, whose covering relations are x_1 < x_2 < ... < x_{a+1} > x_{a+2} > ... > x_{a+b+1} < x_{a+b+2} < ... . We study the associated distributive…

We show that the particle states of Maxwell's theory, in $D$ dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality…

It is believed that Dirichlet series with a functional equation and Euler product of a particular form are associated to holomorphic newforms on a Hecke congruence group. We perform computer algebra experiments which find that in certain…

In this paper we construct combinatorial bases of Feigin-Stoyanovsky's type subspaces of standard modules for level $k$ affine Lie algebra $C_\ell^{(1)}$. We prove spanning by using annihilating field $x_\theta (z)^{k+1}$ of standard…

Let $\mathscr{G}$ be a special parahoric group scheme of twisted type over the ring of formal power series over $\mathbb{C}$, excluding the absolutely special case of $A_{2\ell}^{(2)}$. Using the methods and results of Zhu, we prove a…

In this paper we prove Shapiro's 1958 Conjecture on exponential polynomials, assuming Schanuel's Conjecture.

An update is given on our long-term effort to perform a three-loop check on the Affleck-Alvarez-Manton/Lebedev-Ritus exponentiation conjecture for the imaginary part of the Euler-Heisenberg Lagrangian, using 1+1 dimensional QED as a toy…

Inspired by the idea of blurring the exponential function, we define blurred variants of the $j$-function and its derivatives, where blurring is given by the action of a subgroup of $\rm{GL}_2(\mathbb{C})$. For a dense subgroup (in the…

We test the recently conjectured duality between $N=2$ supersymmetric type II and heterotic string models by analysing a class of higher dimensional interactions in the respective low-energy Lagrangians. These are $F$-terms of the form $F_g…

In this paper, we study a Landis-type conjecture for the general fractional Schr\"{o}dinger equation $((-P)^{s}+q)u=0$. As a byproduct, we also proved the additivity and boundedness of the linear operator $(-P)^{s}$ for non-smooth…

Let $\Gamma$ be a finite rank subgroup of $\overline{\mathbb{Q}}^*$. We prove that the multiplicative group of the field generated by all elements in the divisible hull of $\Gamma$, is free abelian modulo this divisible hull. This proves…

Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory. The 12-dimensional EFT associated to the group $SL(2)\times\mathbb{R}^+$ together with its action is…

We explain how the field of logarithmic-exponential series constructed in \cite{DMM1} and \cite {DMM2} embeds as an exponential field in any field of exponential-logarithmic series constructed in \cite{KK1}, \cite {K} and \cite {KS}. On the…

Extension conjecture states that if a simple module over an artin algebra has nonzero first self-extension group then it has nonzero i-th self-extension group for infinitely many positive integers i. It is shown by recollement of…

The lattice cell in the ${i+1}^{st}$ row and ${j+1}^{st}$ column of the positive quadrant of the plane is denoted $(i,j)$. If $\mu$ is a partition of $n+1$, we denote by $\mu/ij$ the diagram obtained by removing the cell $(i,j)$ from the…

We present a unified algebraic framework utilizing the formal Bell transform to bridge the Dirichlet convolution of arithmetic functions with the combinatorial structure of infinite Euler-type products. By analyzing the logarithmic…

Let us consider a cyclic extension of a function field defined over a finite field. For a character (non-trivial) of this extension, we calculate, as a linear combinations of products of Jacobi sums, the coefficients of the polynomial given…