Related papers: On Fujita's log spectrum conjecture

We prove a Fourier restriction estimate under the assumption that certain convolution power of the measure admits an $r$-integrable density.

We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…

Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…

We study the one-loop effective potential for some Horava-Lifshitz-like theories.

We present a completeness result for the implicit fragment of justification stit logic. Although this fragment allows for no strongly complete axiomatization, we show that a restricted form of strong completeness (subsuming weak…

We show that the subgroup lattice of any finite group satisfies Frankl's Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common…

Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain…

Let $S(t) = \frac{1}{\pi}\Im \log\zeta\left(\frac{1}{2}+it\right)$. We prove an unconditional lower bound on the measure of the sets $\{t\in [T,2T] \colon S(t) \geq V\}$ for $\sqrt{\log\log T} \leq V \ll \left(\frac{\log T}{\log \log…

In the nice recent work [48], S. Wang established uniform log-Sobolev inequalities for mean field particles when the energy is flat convex. In this note we comment how to extend his proof to some semi-convex energies provided the curvature…

In this paper we prove an upper bound for the bottom of the spectrum of the Laplacian on manifolds with Ricci curvature bounded in integral sense. Our arguments rely on the existence of a minimal positive Green's function and its…

We give a conditional proof of the Uniform Boundedness Conjecture of Morton and Silverman in the case of polynomials over number fields, assuming a standard conjecture in arithmetic geometry. Our technique simultaneously yields a dynamical…

Let I be an arbitrary ideal in C[[x,y]]. We use the Newton algorithm to compute by induction the motivic zeta function of the ideal, yielding only few poles, associated to the faces of the successive Newton polygons. We associate a minimal…

In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…

We establish the asymptotic validity of frequency-domain inference for stationary multivariate Hawkes processes under mild conditions, bridging the gap between theory and application. By developing upper-bounds on the reduced cumulant…

We prove that the log canonical threshold of the base ideal of a complete linear system on a complex abelian variety is $\ge 1$, and equality holds if and only if the base locus has divisorial components. Consequently the same assertions…

It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with $C^{1+\varepsilon_-}$-smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for…

We propose a function-field analog of Pisot's $d$-th root conjecture on linear recurrences, and prove it under some "non-triviality" assumption. Besides a recent result of Pasten-Wang on B{\"u}chi's $d$-th power problem, our main tool,…

We determine the spectrum of quantum fluctuations in a 1/2-BPS domain wall version of ABJM theory, thereby enabling the perturbative exploration of the corresponding defect CFT. As expected, the spectrum reflects the supersymmetry of the…

We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding $q$-supercongruence. Similar $q$-supercongruences are established for binomial coefficients and the Ap\'{e}ry numbers, by means of a general…

We consider the binomial distribution with parameters $n$ and $x$, and show that the sum of the squared probabilities is a log-convex function of $x$. This completes the proof of a conjecture formulated in 2014. Applications to R\'{e}nyi…