Related papers: Zero free regions for Dirichlet series

We give an explicit upper bound for non-principal Dirichlet $L$-functions on the line $s=1+it$. This result can be applied to improve the error in the zero-counting formulae for these functions.

There have been, over the last 8 years, a number of far reaching extensions of the famous original F. and M. Riesz's uniqueness theorem that states that if a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has the…

We give explicit upper and lower bounds for $N(T,\chi)$, the number of zeros of a Dirichlet $L$-function with character $\chi$ and height at most $T$. Suppose that $\chi$ has conductor $q>1$, and that $T\geq 5/7$. If…

Let $L(s,f)$ be the $L$-function associated with a newform $f$ of even weight $k$, squarefree level $N$ and trivial nebentypus. In this paper, we establish a new explicit zero-free region for $L(s,f)$. More precisely, we prove that $L(s,f)$…

The Dirichlet divisor problem is used as a model to give a conjecture concerning the conditional convergence of the Dirichlet series of an L-function.

When it comes to partial numerical verification of the Riemann Hypothesis, one crucial part is to verify the completeness of a list of pre-computed zeros. Turing developed such a method, based on an explicit version of a theorem of…

In this paper we give new methods to construct zero divisors in A_n =R^(2^n) the Cayley_Dickson algebras over the real numbers, for n larger than 4, and we also relate the set of zero divisors in A_{n+1} with the Stiefel Manifold V_{2^n…

Let the abstract fractional space-time operator $(\partial_t + A)^s$ be given, where $s \in (0,\infty)$ and $-A \colon \mathsf{D}(A) \subseteq X \to X$ is a linear operator generating a uniformly bounded strongly measurable semigroup…

In this paper we prove existence of (viscosity) solutions of Dirichlet problems concerning fully nonlinear elliptic operator, which are either degenerate or singular when the gradient of the solution is zero. For this class of operators it…

We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other $L$-functions. We establish…

A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structure, plus countably many special…

The purpose of this paper is to characterize the zero sets of holomorphic functions in the Nevanlinna class on a class of convex domains of infinite type in $\mathbb{C}^2$. Moreover, we also obtain $L^p$ estimates, $1 \leq p \leq \infty$,…

We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, R. Xue (2004), we show the…

This paper presents a systematic study for analytic aspects of Fourier-Zernike series of convolutions of functions supported on disks. We then investigate different aspects of the presented theory in the cases of zero-padded functions.

A classical result due to Blaschke states that for every analytic self-map $f$ of the open unit disk of the complex plane there exists a Blaschke product $B$ such that the zero sets of $f$ and $B$ agree. In this paper we show that there is…

We show that central zeros of $L$-functions in the Selberg class have a probabilistic interpretation by stating an equivalence condition of the Riemann hypothesis for the $L$-functions in terms of infinitely divisible distributions.

We study the distribution of zeros of zeta functions associated to Beurling generalized prime number systems whose integers are distributed as $N(x) = Ax + O(x^{\theta})$. We obtain in particular \[ N(\alpha, T) \ll…

We establish a general completeness criterion for Dirichlet-Selberg domains in the symmetric space $SL(n,\mathbb{R})/SO(n)$. By introducing and analyzing Busemann-Selberg functions - which extend classical Busemann functions and capture…

Our main result is to answer a question of Michel Balazard by giving a Dirichlet series with only one zero in its half-plane of convergence. At the end of the paper we also give several sufficient conditions for the Generalized Riemann…

We prove a Bernstein-type inequality involving the Bergman and the Hardy norms, for rational functions in the unit disc \mathbb{D} having at most n poles all outside of \frac{1}{r}\mathbb{D}, 0