相关论文: Collar lemma for Hitchin representations

In the study of automorphic representations over a function field, Hitchin moduli stack and its variants naturally appear and their geometry helps the comparison of trace formulae. We give a survey on applications of this observation to a…

We show that a collar lemma holds for Anosov representations of fundamental groups of surfaces into $\SL(n,\R)$ that satisfy partial hyperconvexity properties inspired from Labourie's work. This is the case for several open sets of Anosov…

The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is…

We study the possible analogous of the Div-Curl Lemma in classical harmonic analysis and partial differential equations, but from the point of view of the multi-parameter setting. In this context we see two possible Div-Curl lemmas that…

We survey the theory of Hitchin representations of Fuchsian groups and describe a conjectural geometric picture of an augmented Hitchin component.

We prove the Jacquet--Rallis fundamental lemma for spherical Hecke algebras over local function fields using multiplicative Hitchin fibrations. Our work is inspired by the proof of [Yun11] in the Lie algebra case and builds upon the general…

With the use of classical statistical argumentation similar to the one used in e.g. statistical optics, it is demonstrated that in entanglement of photons, a classical realist explanation cannot be excluded by the CHSH measure in…

We show that a Hitchin representation is determined by the spectral radii of the images of simple, non-separating closed curves. As a consequence, we classify isometries of the intersection function on Hitchin components of dimension 3 and…

An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the…

In this article we describe the projective representation of Plesken Lie algebras and equivalent central extensions of these algebras. Further it is also shown that there exists a bijective correspondence between second cohomology group,…

In this note we prove a representation theorem for the symmetric cone automorphisms in the spin algebra\, $\Ln$.

The aim of this paper is to give a proof of improving of Zalcman's lemma.

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

In this note, we prove an analog of the Valiron-Titchmarsch Theorem for Positive Temperatures

Let $k$ be a finite field and let $G$ be a reductive group over $k[[\pi]]$. Suppose $\mathrm{char}(k)$ is larger than twice the Coxeter number of $G$, we prove the standard endoscopic fundamental lemma for the spherical Hecke algebra of $G$…

We prove an analogue of the prime number theorem for finite fields.

The aim of this article is to give an elementary proof of the fact that the Schwarz-Pick Lemma follows from the Ahlfors-Schwarz-Pick Lemma.

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

We extend the equivalence of the Salem type for the Riemann hypothesis by application of Titchmarsh's theorem. Other equivalences to the Riemann hypothesis and notes on related Fourier integrals are provided.

The aim of this paper is to give some applications of Zalcman's Rescalling Lemma.