{"docId":98,"paperId":98,"url":"https:\/\/hrj.episciences.org\/98","doi":"10.46298\/hrj.1983.98","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":17,"name":"Volume 6 - 1983"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01104259","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01104259v1","dateSubmitted":"2015-03-03 16:13:38","dateAccepted":"2015-06-12 16:05:17","datePublished":"1983-01-01 08:00:00","titles":{"en":"A note to a paper by Ramachandra on transctndental numbers"},"authors":["Ramachandra, K","Srinivasan, S"],"abstracts":{"en":"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":[{"en":"algebraic numbers"},{"en":"Weierstrass elliptic function"},{"en":"transcendental numbers"},"[MATH] Mathematics [math]"]}