Hasil untuk "math.NT"

Yuchen Ding

We answer negatively a 2014 problem of Yang and Chen on Romanoff type representations. Sharp results involving their problem were also obtained in this article.

Martin Lind

We prove a discrepancy estimate related to the sequence of fractional parts of $b^n/n$. This improves an earlier result of Cilleruelo et al.

Paul M Weichsel

We consider some quadratic variations of the recursive sequence introduced by Lothar Collatz in 1937.

Zhi Qi

In this note, we establish a Voronoï--Oppenheim summation formula for divisor functions over an arbitrary number field.

James Wright

In this paper we introduce two nonlinear functionals, the H and J functional, in the theory of complete exponential sums.

Jorge Mello

We study the extension of a result of Loxton (1972) on representation of algebraic integers as sums of roots of unity to Kummer extensions.

Ajai Choudhry

In this paper we find a parametric solution to the hitherto unsolved problem of finding three positive integers such that their sum, the sum of their squares and the sum of their cubes are simultaneously perfect squares.

Ling Long

In this article, we list a few hypergeometric supercongruence conjectures based on two evaluation formulas of Whipple and numeric data computed using Magma and Sagemath.

Jean Bourgain

We explore the `Moebius disjointness property' in the special context of rank-one transformations and verify this phenomenon for many of the `classical' models

Timothy Foo

We evaluate the Bateman-Horn constant for the polynomial $x^3+x+1$.

Lazhar Fekih-Ahmed

We give new integral and series representations of the Hurwitz zeta function. We also provide a closed-form expression of the coefficients of the Laurent expansion of the Hurwitz-zeta function about any point in the complex plane.

Aleksandar Ivić

We obtain the approximate functional equation for the Rankin-Selberg zeta-function on the 1/2-line.

Nicolas Billerey

Major mistake. The paper has been withdrawn.

Luis Arenas-Carmona

This work is a collection of old and new aplications of Galois cohomology to the clasification of algebraic and arithmetical objects.

Hao Pan

We confirm a conjecture of Sun on the expansions of $n(m^k-1)/(m-1)$ in base $m$.

Luis H. Gallardo

We prove that there are no Wieferich's primes $q=2p+1$ where $p \equiv 3 \pmod{4}$ is a prime number

Gert Almkvist, Arne Meurman

We show that a period polynomial introduced by the Lehmers coincides with a generalized Wilf polynomial.

Diana Savin

We give a necessary condition for the existence of solutions of the Diophantine equation $p=x^{q}+ry^{q},$ with $p$, $q$, $r$ distinct odd prime natural numbers.

Denis Benois

Using the theory of $(\varphi, Γ)$-modules we generalizes Greenberg's construction of the $\Cal L$-invariant to semistable representations

Yuqing Zhang

We apply nondivergence estimates for flows on homogeneous spaces to compute Diophantine exponents of affine subspaces of $\R^n$ and their nondegenerate submanifolds.