10.46298/hrj.1983.98
https://hrj.episciences.org/98
Ramachandra, K
K
Ramachandra
Srinivasan, S
S
Srinivasan
A note to a paper by Ramachandra on transctndental numbers
In this paper, we apply a combinatorial lemma to a well-known result concerning the transcendency of at least one of the numbers $\exp(\alpha_i\beta_j) (i=1, 2, 3; j=1, 2)$, where the complex numbers $\alpha_i,\beta_j$ satisfy linear independence conditions and show that for any $\alpha\neq0$ and any transcendental number $t$, we obtain that at most $\frac{1}{2}+(4N-4+\frac{1}{4})^{1/2}$ of the numbers $\exp(\alpha t^n)~(n=1,2,\ldots,N)$ are algebraic.
Similar statements are given for values of the Weierstrass $\wp$-function and some connections to related results in the literature are discussed.
episciences.org
algebraic numbers
Weierstrass elliptic function
transcendental numbers
[MATH] Mathematics [math]
2015-06-12
1983-01-01
1983-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01104259v1
2804-7370
https://hrj.episciences.org/98/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 6 - 1983
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