相关论文: On the Northcott property for special values of L-…

Pazuki and Pengo defined a Northcott property for special values of zeta functions of number fields and certain motivic $L$-functions. We determine the values for which the Northcott property holds over function fields with constant field…

The Northcott property for special values of Dedekind zeta functions and more general motivic $L$-functions was defined by Pazuki and Pengo. We investigate this property for any complex evaluation of Dedekind zeta functions. The results are…

We study the Northcott and Bogomolov property for special values of Dedekind $\zeta$-functions at real values $\sigma \in \mathbb{R}$. We prove, in particular, that the Bogomolov property is not satisfied when $\sigma \geq \frac{1}{2}$. If…

We give three examples of fields concerning the Northcott property on elements of small height: The first one has the Northcott property but its Galois closure does not satisfy the Bogomolov property. The second one has the Northcott…

In the present paper, we study large values of Dirichlet $L$- functions inside the critical strip. For every $1/2<\sigma<1$, we show that for $q$ sufficiently large, there exists a non-principal character $\chi$ modulo $q$ and a constant…

We consider the joint value distribution of Dirichlet $L$-functions in the critical strip $\frac{1}{2} < \sigma < 1$. We show that the values of distinct Dirichlet $L$-functions are dependent in the sense that they do not behave like…

The problem of finding upper bounds for L-functions at the edge of the critical strip has a long and interesting history. Here, the situation for classical L-functions such as Dirichlet L-functions is relatively well understood. The reason…

We look at the values of two Dirichlet $L$-functions at the Riemann zeros (or a horizontal shift of them). Off the critical line we show that for a positive proportion of these points the pairs of values of the two $L$-functions are…

We introduce a family of L-series specialising to both L-series associated to certain Dirichlet characters over F_q[T] and to integral values of Carlitz-Goss zeta function associated to F_q[T]. We prove, with the use of the theory of…

We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maximum of the Riemann zeta function, or large values of…

We describe in detail three distinct families of generalized zeta functions built over the (nontrivial) zeros of a rather general arithmetic zeta or L-function, extending the scope of two earlier works that treated the Riemann zeros only.…

In this note we investigate the existence of zeros of linear twists of $L$-functions outside of the critical strip. In particular, we show that the Lerch zeta function $L(\lambda,\alpha,s)$ has infinitely many zeros for $1<\sigma<1+\eta$,…

We compute the moments of L-functions of symmetric powers of modular forms at the edge of the critical strip, twisted by the central value of the L-functions of modular forms. We show that, in the case of even powers, it is equivalent to…

We estimate large and small values of $|L(\rho',\chi)|$, where $\chi$ is a primitive character mod $q$ for $q>2$ and $\rho'$ runs over critical points of the Riemann zeta function in the right half of the one-line, that is, the points where…

This paper proposes a conjecture on special values of L-functions of geometric motives over Z. This includes L-functions of mixed motives over Q and Hasse-Weil zeta-functions of schemes over Z. We conjecture the following: the order of L(M,…

In these lectures we first review the important properties of the Riemann $\zeta$-function that are necessary to understand the nature and importance of the Riemann hypothesis (RH). In particular this first part describes the analytic…

In 2011, Gun, Murty and Rath studied non-vanishing and transcendental nature of special values of a varying class of $L$-functions and their derivatives. This led to a number of works by several authors in different set-ups including…

Let $\mathcal{M}$ be a pure motive over $\mathbb{Q}$ of odd weight $w\geq 3$, even rank $d\geq 2$, and global conductor $N$ whose $L$-function $L(s,\mathcal{M})$ coincides with the $L$-function of a self-dual algebraic tempered cuspidal…

A set of algebraic numbers has the Northcott property if each of its subsets of bounded Weil height is finite. Northcott's Theorem, which has many Diophantine applications, states that sets of bounded degree have the Northcott property.…

We establish new explicit zero-free regions for the Dedekind zeta-function. Two key elements of our proof are a non-negative, even, trigonometric polynomial and explicit upper bounds for the explicit formula of the so-called differenced…