相关论文: Zeros of $L$-Functions in Low-Lying Intervals and …
In this note we prove that, for $p>0$, $L_{p}[0,1]\smallsetminus\bigcup_{q\in(p,\infty)}L_{q}[0,1]$ is $(\alpha,\mathfrak{c})$-spaceable if, and only if, $\alpha<\aleph_{0}$. Such a problem first appears in [V. F\'avaro, D. Pellegrino, D.…
Consider the viscous Burgers equation on a bounded interval with inhomogeneous Dirichlet boundary conditions. Following the variational framework introduced by Bertini-De Sole-Gabrielli-Jona-Lasinio-Landim C, we analyze a Lyapunov…
The paper shows that for any $G_\delta$ set $F$ of Lebesgue measure zero on the unit circle $T$ there exists a function $f \in H^{\infty}$ such that the radial limits of $f$ exist at each point of $T$ and vanish precisely on $F$. This…
In this paper we find extremal one-sided approximations of exponential type for a class of truncated and odd functions with a certain exponential subordination. These approximations optimize the $L^1(\mathbb{R}, |E(x)|^{-2}dx)$-error, where…
We study the low lying zeros of $GL(2) \times GL(2)$ Rankin-Selberg $L$-functions. Assuming the generalized Riemann hypothesis, we compute the $1$-level density of the low-lying zeroes of $L(s, f \otimes g)$ averaged over families of…
We provide an abstract framework for a Logvinenko-Sereda type theorem, where the classical compactness assumption on the support of the Fourier transform is replaced by the assumption that the functions under consideration belong to a…
We give universal bounds on the fraction of nontrivial zeros having given multiplicity for L-functions attached to a cuspidal automorphic representation of $\mathrm{GL}_m/\mathbb{Q}$. For this, we apply the higher-level correlation…
Bennett, DeVore and Sharpley introduced the space weak $L^{\infty}$ in 1981 and studied its relationship with functions of bounded mean oscillation. Here we characterize weak $L^{\infty}$ in measure spaces without using the decreasing…
We slightly improve the lower bound of Baez-Duarte, Balazard, Landreau and Saias in the Nyman-Beurling formulation of the Riemann Hypothesis as an approximation problem. We construct Hilbert space vectors which could prove useful in the…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
The de Branges-Rovnyak space $H(b)$ is generated by a bounded analytic function $b$ in the unit ball of $H^\infty$. When $b$ is a nonextreme point, the space $H(b)$ is invariant by the forward shift operator $M_z$. We show that the $H(b)$…
This text shows the existence of large (3.54 times the average) gaps between consecutive zeros, on the critical line, of some Dirichlet $L$-functions $L(s,\chi),$ with $\chi$ being an even primitive Dirichlet character.
In this paper, we prove some zero density theorems for certain families of Dirichlet $L$-functions. More specifically, the subjects of our interest are the collections of Dirichlet $L$-functions associated with characters to moduli from…
New Hardy and Sobolev type inequalities involving $L^1$-norms of scalar and vector-valued functions in $\Bbb{R}^n$ are obtained. The work is related to some problems stated in the recent paper by Bourgain and Brezis
We establish unconditional sharp upper bounds of the $k$-th moments of the family of quadratic Dirichlet $L$-functions at the central point for $0 \leq k \leq 2$.
We characterize all linear operators which preserve spaces of entire functions whose zeros lie in a closed strip. Necessary and sufficient conditions are obtained for the related problem with real entire functions, and some classical…
Given an $L$-function, one of the most important questions concerns its vanishing at the central point; for example, the Birch and Swinnerton-Dyer conjecture states that the order of vanishing there of an elliptic curve $L$-function equals…
The generalized Young inequality on the Lorentz spaces for commutative hypergroups is introdused and an application of it is given to the theory of fractional integrals. The boundedness on the Lorentz space and the Hardy-Littlewood-Sobolev…
Inner functions are an important and popular object of study in the field of complex function theory. We look at meromorphic inner functions with a given spectrum and provide sufficient conditions for them to have uniformly bounded…
We show that the weak limit of a quasiminimizing sequence is a quasiminimal set. This generalizes the notion of weak limit of a minimizing sequences introduced by De Lellis, De Philippis, De Rosa, Ghiraldin and Maggi. This result is also…