Centro de Ciencias Matemáticas

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20042020

most citedCovariance in models of loop quantum gravity: Spherical symmetry

109 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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11 papers · 1 filter

math.NT2020★ 2 cited

Truncated $t$ -adic symmetric multiple zeta values and double shuffle relations

Masataka Ono, Shin-ichiro Seki, Shuji Yamamoto

We study a refinement of the symmetric multiple zeta value, called the $t$ -adic symmetric multiple zeta value, by considering its finite truncation. More precisely, two kinds of re…

math.NT2020★ 4 cited

On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences

Mahadi Ddamulira, Florian Luca

Let $r \geq 1$ be an integer and $U := (U_{n})_{n \geq 0}$ be the Lucas sequence given by $U_{0} = 0$ , $U_{1} = 1,$ and $U_{n + 2} = r U_{n + 1} + U_{n}$ , for all $n \geq 0$ . In this paper, we show…

math.NT2019★ 15 cited

On the problem of Pillai with $k$ --generalized Fibonacci numbers and powers of $3$

Mahadi Ddamulira, Florian Luca

For an integer $k \geq 2$ , let ${F_{n}^{(k)}}_{n \geq 2 - k}$ be the $k$ --generalized Fibonacci sequence which starts with $0, \dots, 0, 1$ (a total of $k$ terms) and for which each t…

math.NT2018

Double exponential sums and congruences with intervals and exponential functions modulo a prime

M. Z. Garaev

Let $p$ be a large prime number and $g$ be any integer of multiplicative order $T$ modulo $p$ . We obtain a new estimate of the double exponential sum $$ S=\sum_{n\in \mathcal{N}}\l…

math.NT2016★ 8 cited

Diophantine triples with values in $k$ -generalized Fibonacci sequences

Clemens Fuchs, Christoph Hutle, Florian Luca +1

We show that if $k \geq 2$ is an integer and $(F_{n}^{(k)})_{n \geq 0}$ is the sequence of $k$ -generalized Fibonacci numbers, then there are only finitely many triples of positive intege…

math.NT2015★ 4 cited

Sylvester's Theorem and the Non-integrality of a certain Binomial Sum

Daniel López-Aguayo, Florian Luca

In this note, we show that $S (n, r) := \sum_{k = 0}^{n} (k n) \frac{k}{k + r}$ is not an integer for any positive integer $n$ and $r \in {1, 2, 3, 4, 5, 6}$ and for $n \leq r - 1$ . This giv…

math.NT2014★ 30 cited

Congruences involving product of intervals and sets with small multiplicative doubling modulo a prime and applications

J. Cilleruelo, M. Z. Garaev

In the present paper we obtain new upper bound estimates for the number of solutions of the congruence $$ x\equiv y r\pmod p;\quad x,y\in \mathbb{N},\quad x,y\le H,\quad r\in\cU, $…

math.NT2013★ 14 cited

On equal values of power sums of arithmetic progressions

A. Bazsó, D. Kreso, F. Luca +1

In this paper we consider the Diophantine equation \begin{align*}b^k +\left(a+b\right)^k &+ \cdots + \left(a\left(x-1\right) + b\right)^k=\\ &=d^l + \left(c+d\right)^l + \cdots + \…

math.NT2013

Multiplicative decomposition of arithmetic progressions in prime fields

M. Z. Garaev, S. V. Konyagin

We prove that there exists an absolute constant $c > 0$ such that if an arithmetic progression $\cP$ modulo a prime number $p$ does not contain zero and has the cardinality less than…

math.NT2013★ 1 cited

Kloosterman sums in residue rings

J. Bourgain, M. Z. Garaev

In the present paper, we generalize some of the results on Kloosterman sums proven in \cite{BG} for prime moduli to general moduli. This requires to establish the corresponding add…

math.NT2012★ 5 cited

On the Counting Function of Elliptic Carmichael Numbers

Florian Luca, Igor E. Shparlinski

We give an upper bound for the number elliptic Carmichael numbers $n \leq x$ that have recently been introduced by J. H. Silverman. We also discuss several possible ways for further…

Truncated t-adic symmetric multiple zeta values and double shuffle relations