Related papers: Non-commutative q-expansions

We define the zeta function of a noncommutative K3 surface over a finite field, an invariant under Fourier-Mukai equivalence that can be used to define point counts in this noncommutative setting. These point counts can be negative, and can…

q-oscillators are associated to the simplest non-commutative example of Hopf algebra and may be considered to be the basic building blocks for the symmetry algebras of completely integrable theories. They may also be interpreted as a…

The classical model of q-damped oscillator is introduced and solved in terms of Jackson q-exponential function for three different cases, under-damped, over-damped and the critical one. It is shown that in all three cases solution is…

In this article we will derive a combinatorial formula for the partition function p(n). In the second part of the paper we will establish connection between partitions and q-binomial coefficients and give new interpretation for q-binomial…

We prove a formula (analogous to that of Kida in classical Iwasawa theory and generalizing that of Hachimori-Matsuno for elliptic curves) giving the analytic and algebraic p-adic Iwasawa invariants of a modular eigenform over an abelian…

We study the properties of a function $\psi(z, q)$ (the generalized polygamma function), intimately connected with the Hurwitz zeta function and defined for complex values of the variables $z$ and $q$, which is entire in the variable $z$…

In a previous work we have introduced the notion of embedded $\Q$-resolution, which essentially consists in allowing the final ambient space to contain abelian quotient singularities. Here we give a generalization of N. A'Campo's formula…

Recently Iwasawa theory for graphs is developing. A significant achievement includes an analogue of Iwasawa class number formula, which describes the asymptotic growth of the numbers of spanning trees for $\mathbb{Z}_p$-coverings of graphs.…

The asymptotic behavior of a nonlinear diffusive equation obtained in the framework of the $\kappa$-generalized statistical mechanics is studied. The analysis based on the classical Lie symmetry shows that the $\kappa$-Gaussian function is…

In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function $F(q)$ of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan's mock…

The purpose of this paper is to prove the main conjecture of non-commutative Iwasawa theory for p-adic Lie extensions, for an odd prime p, of totally real number fields assuming that the Iwasawa mu invariant of a certain totally real number…

This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.

We derive the correction due to noncommutativity of space on Born approximation, then the correction for the case of Yukawa potential is explicitly calculated. The correction depends on the angle of scattering. Using partial wave method it…

We express the $q$-Pochhammer symbol $(z;q)_\infty$ as an infinite product of gamma functions, analogously to how Narukawa expressed the elliptic gamma function as an infinite product of hyperbolic gamma functions. This identity is used to…

Let $\Gamma$ be a cocompact, oriented Fuchsian group which is not on an explicit finite list of possible exceptions and $q$ a sufficiently large prime power not divisible by the order of any non-trivial torsion element of $\Gamma$. Then…

In this paper, we analyze the solutions of the following non-linear differential-difference equations f^n(z) +\omega f^(n-1)f'(z) +p(z)f(z+c) = p_1e^{\alpha}_1z +p_2e^{\alpha}_2z and f^n(z)f'(z) +q(z)e^Q(z)f(z+c) = p_1e^{\alpha}_1z…

Let p be an odd prime. We give an unconditional proof of the equivariant Iwasawa main conjecture for totally real fields for an infinite class of one-dimensional non-abelian p-adic Lie extensions. Crucially, this result does not depend on…

We give an explicit formula of the coefficients of the Zeta-Function's L-polynomial for algebraic function fields over finite constant fields. Thus, we deduce an expression of the class number of algebraic function fields defined over…

This paper contains a complete proof of Fukaya's and Kato's epsilon$-isomorphism conjecture in [23] for invertible \Lambda-modules (the case of V = V_0(r) where V_0 is unramified of dimension 1). Our results rely heavily on Kato's…

We propose an evolution equation for unintegrated gluon densities that is valid for large values of the QCD coupling constant $\bar{\alpha} _s$. Our approach is based on the linear resummation model introduced by Sta\'{s}to. We generalize…