相关论文: Lochs-type theorems beyond positive entropy

Langlands' functoriality principle predicts deep relations between the local and automorphic spectra of different reductive groups. This has been generalized by the relative Langlands program to include spherical varieties, among which…

The main goal of this thesis is to develop the integration theory of curved homotopy Lie algebras. In the first chapter, we develop the operadic calculus needed: we encode non-necessarily conilpotent coalgebras with operads and introduce…

In the function field setting with a fixed characteristic, it was proven by the second and third authors that the values $\log \big|L\big(\frac12, \chi_D\big)\big|$ as $D$ varies over monic and square-free polynomials are asymptotically…

We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of…

In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…

The Tsallis-Cirto non-extensive statistics with $\delta=2$ describes the processes of splitting and merging of black holes and their thermodynamics. Here we consider a toy model, which matches this generalized statistics and extends it by…

In various contexts in mathematical physics one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the…

Black holes in equilibrium and the counting of their entropy within Loop Quantum Gravity are reviewed. In particular, we focus on the conceptual setting of the formalism, briefly summarizing the main results of the classical formalism and…

The Clark theorem is important in critical point theory. For a class of even functionals it ensures the existence of infinitely many negative critical values converging to $0$ and it has important applications to sublinear elliptic…

AdS_2/CFT_1 correspondence predicts that the logarithm of a Z_N twisted index over states carrying a fixed set of charges grows as 1/N times the entropy of the black hole carrying the same set of charges. In this paper we verify this…

The purpose of this paper is to generalize our earlier work on the logarithm of the Riemann zeta-function to linear combinations of logarithms of primitive Dirichlet $L$-functions with constant real coefficients. Under the assumption of…

The Boolean lattice of logical statements induces the free distributive lattice of questions. Inclusion on this lattice is based on whether one question answers another. Generalizing the zeta function of the question lattice leads to a…

The entanglement entropy and the logarithmic negativity can be computed in quantum field theory through a method based on the replica limit. Performing these analytic continuations in some cases is beyond our current knowledge, even for…

Several years ago, it has been discussed that non-logarithmic entropies such as the Tsallis q-entropy cannot be applied to systems with continuous variables. Now, in their recent paper [Phys. Rev. E 97, 012104 (2018)], Oikonomou and Bagci…

By a re-examination of MacMahon's original proof of his celebrated theorem on the distribution of the major indices over permutations, we give a reformulation of his argument in terms of the structure of labeled partitions. In this…

We prove some new log-free density theorems for zeros of Dirichlet L-functions (which accordingly are more sharp than earlier ones near to the boundary line of the critical strip). The results can be applied in several problems of prime…

This chapter deals with our recent attempt to extend the notion of equilibrium (EQ) entropy to nonequilibrium (NEQ) systems so that it can also capture memory effects. This is done by enlarging the equilibrium state space by introducing…

This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of…

The classical Gauss--Lucas theorem describes the location of the critical points of a polynomial. There is also a hyperbolic version, due to Walsh, in which the role of polynomials is played by finite Blaschke products on the unit disk. We…

In this paper, we examine a generic theory of 1+1-dimensional gravity with coupling to a scalar field. Special attention is paid to a class of models that have a power-law form of dilaton potential and can capably admit black hole…