P. Letendre

activity

20182020

most citedThe number of integer points close to a polynomial

1 citations · 1 across the 5 of their papers we have counts for

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7 papers · 1 filter

math.NT2020

A hybrid inequality for the number of divisors of an integer

Patrick Letendre

We establish an explicit inequality for the number of divisors of an integer $n$ . It uses the size of $n$ and its number of distinct prime divisors.

math.NT2019

Polynomials with integer roots

Patrick Letendre

Let $F_{n}$ be the set of unitary polynomials of degree $n \geq 2$ that have their roots in $Z^{*}$ . We note $Q (x) := x^{n} + a_{1} x^{n - 1} + \dots + a_{n} .$ We show that…

math.NT2019

Subsets of $F_{p}^{*}$ with only small products or ratios

Patrick Letendre

Let $p$ be a fixed prime. We estimate the number of elements of a set $A \subseteq F_{p}^{*}$ for which $$ s_1s_2 \equiv a \pmod{p} \quad \mbox{for some}\quad a \in [-X,X] \qu…

math.NT2019

Truncated convolution of Möbius function and multiplicative energy of an integer $n$

Patrick Letendre

We establish an interesting upper bound for the moments of truncated Dirichlet convolution of Möbius function, a function noted $M (n, z)$ . Our result implies that $M (n, j)$ is usuall…

math.NT2019★ 1 cited

The number of integer points close to a polynomial

Patrick Letendre

Let $f (x)$ be a polynomial of degree $n \geq 1$ with real coefficients and let $X \geq 2$ and $δ \geq 0$ be real numbers. Let $∥ \cdot ∥$ be the distance to the nearest integer. We obt…

math.NT2018

New upper bounds for the number of divisors function

Jean-Marie De Koninck, Patrick Letendre

Let $τ (n)$ stand for the number of divisors of the positive integer $n$ . We obtain upper bounds for $τ (n)$ in terms of $lo g n$ and the number of distinct prime factors of $n$ .

A hybrid inequality for the number of divisors of an integer

Polynomials with integer roots

Subsets of Fp∗​ with only small products or ratios

Truncated convolution of Möbius function and multiplicative energy of an integer n

The number of integer points close to a polynomial

New upper bounds for the number of divisors function

Subsets of $F_{p}^{*}$ with only small products or ratios

Truncated convolution of Möbius function and multiplicative energy of an integer $n$