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Independence results for pattern sequences in distinct bases

100%

Tachiya Y.

Acta Arithmetica

2010

tom 142

nr 2

157-167

Explicit algebraic dependence formulae for infinite products related with Fibonacci and Lucas numbers

51%

Kaneko H., Kurosawa T., Tachiya Y., Tanaka T.-a.

Acta Arithmetica

2015

tom 168

nr 2

161-186

Let d ≥ 2 be an integer. In 2010, the second, third, and fourth authors gave necessary and sufficient conditions for the infinite products $∏_{k=1 \atop U_{d^k}≠-a_i}^{∞} (1 + (a_i)/(U_{d^k}))$ (i=1,...,m) or $∏_{k=1 \atop V_{d^k}≠-a_i}^{∞} (1 + (a_i)(V_{d^k})$ (i=1,...,m) to be algebraically dependent, where $a_i$ are non-zero integers and $U_n$ and $V_n$ are generalized Fibonacci numbers and Lucas numbers, respectively. The purpose of this paper is to relax the condition on the non-zero integers $a_1,...,a_m$ to non-zero real algebraic numbers, which gives new cases where the infinite products above are algebraically dependent.

Ograniczanie wyników

2 Acta Arithmetica

2 Tachiya Y.

1 Kaneko H.

1 Kurosawa T.

1 Tanaka T.-a.

1 2015

1 2010

Wyniki wyszukiwania

Independence results for pattern sequences in distinct bases

Explicit algebraic dependence formulae for infinite products related with Fibonacci and Lucas numbers