Results 1 to 10 of about 769 (62)

Diophantine approximation with one prime, two squares of primes and one kth power of a prime

Open Mathematics, 2021
Let ...
Gambini Alessandro
doaj   +1 more source

The integral part of a nonlinear form with a square, a cube and a biquadrate

Open Mathematics, 2020
In this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{
Ge Wenxu, Li Weiping, Zhao Feng
doaj   +1 more source

One Diophantine inequality with unlike powers of prime variables

Journal of Inequalities and Applications, 2016
In this paper, we show that if λ 1 $\lambda_{1}$ , λ 2 $\lambda_{2}$ , λ 3 $\lambda_{3}$ , λ 4 $\lambda _{4}$ , λ 5 $\lambda_{5}$ are nonzero real numbers not all of the same sign, η is real, 0 < σ < 1 720 ...
Wenxu Ge, Weiping Li
doaj   +1 more source

A note on Diophantine inequalities in function fields [PDF]

Notes on Number Theory and Discrete Mathematics
We will discuss how the Bentkus–Götze–Freeman variant of the Davenport–Heilbronn circle method can be used to study 𝔽_q[t] solutions to inequalities of the form ord(λ₁p₁ᵏ+...+λₛpₛᵏ-γ)
Kathryn Wilson
doaj   +1 more source

On the Olson and the Strong Davenport constants [PDF]

, 2010
A subset $S$ of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of $S$ is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant.
Ordaz, Oscar, Philipp, Andreas, Santos, Irene, Schmid, Wolfgang A.   +3 more
core   +4 more sources

On Diophantine approximation by unlike powers of primes

Open Mathematics, 2019
Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irrational, λ2/λ4 and λ3/λ5 are rational. Let η real, and ε > 0.
Ge Wenxu, Li Weiping, Wang Tianze
doaj   +1 more source

The density of discriminants of quintic rings and fields [PDF]

, 2010
We determine, asymptotically, the number of quintic fields having bounded discriminant. Specifically, we prove that the asymptotic number of quintic fields having absolute discriminant at most X is a constant times X.
Bhargava, Manjul
core   +1 more source

Transcendental equations satisfied by the individual zeros of Riemann $\zeta$, Dirichlet and modular $L$-functions [PDF]

, 2015
We consider the non-trivial zeros of the Riemann $\zeta$-function and two classes of $L$-functions; Dirichlet $L$-functions and those based on level one modular forms.
França, Guilherme, LeClair, André
core   +1 more source

Approximation to points in the plane by SL(2,Z)-orbits [PDF]

, 2010
Let x be a point in R^2 with irrational slope and let \Gamma denote the lattice SL(2,Z) acting linearly on R^2. Then, the orbit \Gamma x is dense in R^2.
Laurent, Michel, Nogueira, Arnaldo
core   +2 more sources