Related papers: Chebotar\"ev Density and the Bateman-Horn constant
We discuss various effective forms of Chebotarev's density theorem, answering a question of Serre and a question of Murty, Murty and Seradha.
In this short note, we show an analogue of Dawsey's formula on Chebotarev densities for finite Galois extensions of $\mathbb{Q}$ with respect to the Riemann zeta function $\zeta(ms)$ for any integer $m\geqslant2$. Her formula may be viewed…
An old open problem in number theory is whether Chebotarev density theorem holds in short intervals. More precisely, given a Galois extension $E$ of $\mathbb{Q}$ with Galois group $G$, a conjugacy class $C$ in $G$ and an $1\geq…
This is an expository paper discussing various versions of Khovanov homology theories, interrelations between them, their properties, and their applications to other areas of knot theory and low-dimensional topology.
The effective version of Chebotarev's density theorem under the Generalized Riemann Hypothesis and the Artin conjecture (cf. Iwaniec and Kowalski's Analytic Number Theory, 5.13) involves a numerical invariant of a subset $D$ of a finite…
Depending on the recent experiments and some new way of explaining electron we have developed here equations for velocities of different mode with the charge density. This includes as well how the charge-density can be distributed in the…
We evaluate the Bateman-Horn constant for the polynomial $x^3+x+1$.
We describe some studies related to the frequency of prime values of integer polynomials.
This an expository article on Givental's axiomatic Gromov--Witten theory and some of its applications.
For a fixed number field $K$, we consider the mean square error in estimating the number of primes with norm congruent to $a$ modulo $q$ by the Chebotar\"ev Density Theorem when averaging over all $q\le Q$ and all appropriate $a$. Using a…
We show that first approximations to the bulk viscosity $\eta_v$ are expressible in terms of factors that depend on the sound speed $v_s$, the enthalpy, and the interaction (elastic and inelastic) cross section. The explicit dependence of…
In this short note, we address a gap in the proof of Sauvageot's density principle, which was pointed out in a paper by Nelson-Venkatesh.
This article covers three topics. (1) It establishes links between the density of certain subsets of the set of primes and related subsets of the set of natural numbers. (2) It extends previous results on a conjecture of Bruinier and Kohnen…
We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the dynamical Casimir emission of pairs of Bogoliubov phonons when the atom-atom scattering length is modulated in time.…
In this paper some links between the density of a set of integers and the density of its sumset, product set and set of subset sums are presented.
In the first part we construct some Buck measurable sets. In the second part we apply the Niven theorem for Buck's measure density to certain sets.
In this paper we find lower bounds on higher moments of the error term in the Chebotarev density theorem. Inspired by the work of Bella\''{\i}che, we consider general class functions and prove bounds which depend on norms associated to…
This is the second of three papers about the Compression Theorem. We give proofs of Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer--Verlag (1986); 2.4.5 C'] and of the Normal Deformation Theorem…
In this paper we give a conjectural refinement of the Davenport-Heilbronn theorem on the density of cubic field discriminants. We explain how this refinement is plausible theoretically and agrees very well with computational data.
We estimate bulk and shear viscosity at finite temperature and baryon densities of hadronic matter within hadron resonance gas model. For bulk viscosity we use low energy theorems of QCD for the energy momentum tensor correlators. For shear…