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math.NT2025
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.
math.NT2025
Three-term Machin-type formulae
Tomohiro Yamada
We shall show that there exist only finitely many nondegenerate three-term Machin-type formulae and give explicit upper bounds for the sizes of variables.
math.NT2024
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…