Related papers: Some extensions in the Adams spectral sequence and…

For the tensor field of rank-2 there are two unitary irreducible representation (UIR) in de Sitter (dS) space denoted by $\Pi^{\pm}_{2,2}$ and $\Pi^{\pm}_{2,1}$ [1]. In the flat limit only the $\Pi^{\pm}_{2,2}$ coincides to the UIR of…

We study asymptotics of fiber integrals depending on a large parameter. When the critical fiber is singular, full-asymptotic expansions are established in two different cases : local extremum and isolated real principal type singularities.…

We first provide a classical analysis proof of a version of the Alexandroff-Bakelman-Pucci inequality (ABP) for compactly supported $C^2$ functions in dimension $2$, inspired by the symplectic geometry proof method of Viterbo, which avoids…

A representation for the Riemann zeta function valid for arbitrary complex $s=\sigma+it$ is $\zeta(s)=\sum_{n=0}^\infty A(n,s)$, where \[A(n,s)=\frac{2^{-n-1}}{1-2^{1-s}} \sum_{k=0}^n \left(\!\begin{array}{c}n\\k\end{array}\!\right)…

20-component Petras theory of 1/2-spin particle with anomalous magnetic momentum in presence of external electromagnetic and gravitational fields is investigated. The gravitation field is described as space-time curvature. Correctness of…

A new parametric integral is obtained as a consequence of the Riemann hypothesis. An asymptotic multiplicability is the main property of this integral.

The Riemann Hypothesis (RH) - that all nonreal zeros of Riemann's zeta function shall have real part 1/2 - remains a major open problem. Its most concrete equivalent is that an infinite sequence of real numbers, the Keiper--Li constants,…

We present a short, purely algebraic proof of the Symmetric Bessmertny\u{i} Realization Theorem in the characteristic $2$ case recently proved in [EOW26]. Symmetric Bessmertny\u{i} realizations are Schur complements of affine linear…

Localized at almost all primes, we describe the structure of differentials in several important spectral sequences that compute the cohomology of classifying spaces of topological Kac-Moody groups. In particular, we show that for all but a…

An algorithm is described giving effective determination of the second differential in the Adams spectral sequence. The algorithm is based on the notion of secondary derived functor, and on the explicit algebraic model of the groupoid…

We show Green's function asymptotic upper bound for the two-point function of weakly self-avoiding walk in dimension bigger than 4, revisiting a classic problem. Our proof relies on Banach algebras to analyse the lace-expansion fixed point…

We give a tool for understanding simplicial desuspension in A1-algebraic topology: we show that $X \to \Omega (S^1 \wedge X)\to \Omega (S^1 \wedge X \wedge X)$ is a fiber sequence up to homotopy in 2-localized A1-algebraic topology for $X =…

Let p be a prime number, and let K be a number field. For p=2, assume moreover K totally imaginary. In this note we prove the existence of asymptotically good extensions L{K of cohomological dimension 2 in which infinitely many primes split…

In this paper, we establish an abstract infinite dimensional KAM theorem dealing with normal frequencies in weaker spectral asymptotics \Omega_{i}(\xi)=i^d+o(i^{d})+o(i^{\delta}), where $d>0, \delta<0$, which can be applied to a large class…

In 2018, Kahle and Stump raised the following problem: identify sequences of finite Coxeter groups $W_n$ for which the two-sided descent statistics on a uniform random element of $W_n$ is asymptotically normal. Recently, Br\"uck and…

In this paper, we consider rational hypergeometric series of the form \[\frac{p}{\pi}= \sum_{k=0}^\infty u_k\quad\text{with}\quad u_k=\frac{\left(\frac{1}{2}\right)_k \left(q\right)_k \left(1-q\right)_k}{(k!)^3}(r+s\,k)\,t^k,\] where…

The problem of Gamma + Pi --> Pi + Pi is studied using the axial anomaly, elastic unitarity, analyticity and crossing symmetry. Single variable dispersion relation is assumed. Using elastic unitarity relation, an integral equation equation…

In this paper, we establish the asymptotic expansion at infinity of gradient graph in dimension 2 with vanishing mean curvature at infinity. This corresponds to our previous results in higher dimensions and generalizes the results for…

In this paper we constructs a new nontrivial family in the stable homotopy groups of spheres $\pi_{p^nq+2pq+q-3}S$ which is of order $p$ and is represented by $k_0h_{n} \in Ext_A^{3,p^nq+2pq+q}(\mathbb{Z}_p,\mathbb{Z}_p)$ in the Adams…

Equations for 16-component vector-bispinor field, originated from Rarita-Schwinger Lagrangian for spin 3/2 field extended to Riemannian space-time are investigated. Additional general covariant constrains for the field are produced, which…