T. Yamada

activity

20032023

most citedExplicit formulae for primes in arithmetic progressions, I

7 citations · 26 across the 27 of their papers we have counts for

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27 papers · 1 filter

math.NT2023

On Lehmer's problem and related problems

Tomohiro Yamada

We show that if $N \pm 1 = M φ (N)$ with $N \neq = 15, 255$ composite, then $M < 15.76515 lo g lo g lo g N$ and $M < 16.03235 lo g lo g ω (N)$ , together with similar results for the unitary totient f…

math.NT2021

Explicit sieve estimates and nonexistence of odd multiperfect numbers of a certain form

Tomohiro Yamada

We prove explicit asymptotic formulae for some functions used in sieve methods and show that there exists no odd multiperfect number of abundancy four whose squared part is cubefre…

math.NT2020

Necessary conditions for binomial collisions

Tomohiro Yamada

We shall give some necessary conditions for the equation $(a x) = (b y)$ to hold: if $(n - m 2 n + δ) = (n - k 2 n + l)$ with $δ = 0$ or $1$ , $0 < m \leq 0.735 k$ , $k < n$ an…

math.NT2019

On Sinha's note on perfect numbers

Tomohiro Yamada

We shall show that there is no odd perfect number of the form $2^{n} + 1$ or $n^{n} + 1$ .

math.NT2019

On a problem of De Koninck

Tomohiro Yamada

Let $σ (n)$ and $γ (n)$ denote the sum of divisors and the product of distinct prime divisors of $n$ respectively. We shall show that, if $n \neq = 1, 1782$ and $σ (n) = (γ (n))^{2}$ , then th…

math.NT2019

A note on linear forms in two logarithms: the argument of an algebraic power

Tomohiro Yamada

In this note, we shall give an improved lower bound for the argument of a power of a given algebraic number which has absolute value one but is not a root of unity.