Related papers: Symbolic dynamics and rotation symmetric Boolean f…
Rotation symmetric Boolean functions are invariant under circular translation of indices. These functions have very rich cryptographic properties and have been used in different cryptosystems. Recently, Thomas Cusick proved that exponential…
In this text we introduce and analyze families of symmetric functions arising as partition functions for colored fermionic vertex models associated with the quantized affine Lie superalgebra $U_q \big( \widehat{\mathfrak{sl}} (1 | n)…
We give a geometric description of the motion of eigenvalues of a Brownian motion with values in some matrix spaces. In the second part we consider a paper by Polya where he introduced a function close to the Riemann zeta function, which…
The appearance of multiple zeta values in anomalous dimensions and $\beta$-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we…
This is the second paper in a series where we study arithmetic applications of the multiple elliptic Gamma functions originated in mathematical physics. In the first article in this series we defined geometric families of these functions…
Wetterich's equation provides a powerful tool for investigating the existence and universal properties of renormalization group fixed points exhibiting quantum scale invariance. Motivated by recent works on asymptotically safe scalar-tensor…
Rotation symmetric Boolean functions have important applications in the design of cryptographic algorithms. In this paper, the Conjecture about rotation symmetric Boolean functions (RSBFs) of degree 3 proposed by Cusik and St\u{a}nic\u{a}…
In this paper we introduce an equivalence relation on the classes of almost periodic functions of a real or complex variable which is used to refine Bochner's result that characterizes these spaces of functions. In fact, with respect to the…
Weights of permutations were originally introduced by Dugan, Glennon, Gunnells, and Steingr\'imsson (Journal of Combinatorial Theory, Series A 164:24-49, 2019) in their study of the combinatorics of tiered trees. Given a permutation…
We construct variants of the Riemann zeta function with convenient properties and make conjectures about their dynamics; some of the conjectures are based on an analogy with the dynamical system of zeta. More specifically, we study the…
Among solutions of n-Gelfand-Dikii's hierarchy there exists a remarkable solution W, which satisfies the string equation. We call it Witten's solution because according to the Witten conjecture the function F(x_1, x_2, x_3,...) =…
In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space $E_n$ are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a…
The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…
Drawing on analogies with the commutative case, the Wilsonian picture of renormalization is developed for noncommutative scalar field theory. The dimensionful noncommutativity parameter, theta, induces several new features. Fixed-points are…
We prove certain general forms of functional relations among Witten multiple zeta-functions in several variables (or zeta-functions of root systems). The structural background of those functional relations is given by the symmetry with…
The special uniformity of zeta functions claims that pure non-abelian zeta functions coincide with group zeta functions associated to the special linear groups. Naturally associated are three aspects, namely, the analytic, arithmetic, and…
With tools of measure theory and symbols of matrix sequences, we explore the results regarding curves on finite fields and Weil Systems. This document wants to draw a bridge between the two areas and link the concepts of distribution of…
Rotation symmetric Boolean functions represent an interesting class of Boolean functions as they are relatively rare compared to general Boolean functions. At the same time, the functions in this class can have excellent properties, making…
Homogeneous rotation symmetric Boolean functions have been extensively studied in recent years because of their applications in cryptography. Little is known about the basic question of when two such functions are affine equivalent. The…
We present a comprehensive discussion of tree-level holographic $4$-point functions of scalar operators in momentum space. We show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus a valid…