HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

# A note to a paper by Ramachandra on transctndental numbers

Abstract : 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.
Keywords :
Document type :
Journal articles
Domain :

Cited literature [4 references]

https://hal.archives-ouvertes.fr/hal-01104259
Contributor : Ariane Rolland Connect in order to contact the contributor
Submitted on : Friday, January 16, 2015 - 2:14:01 PM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM
Long-term archiving on: : Friday, September 11, 2015 - 6:57:35 AM

### File

6Article3.pdf
Explicit agreement for this submission

### Citation

K Ramachandra, S Srinivasan. A note to a paper by Ramachandra on transctndental numbers. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 1983, Volume 6 - 1983, pp.37 - 44. ⟨10.46298/hrj.1983.98⟩. ⟨hal-01104259⟩

Record views