Skip to main content
Article thumbnail
Location of Repository

Let Tq(z) = ∑ ∞

By Mr (b: J, K. (fin-oul) Zudilin and V. V. (rs-mosc

Abstract

ν=0 q−ν(ν+1)/2 z ν, |q |> 1, be the Chakalov (or Tschakaloff) series. The authors prove the linear independence of the numbers 1, T q t 1(α) and T q t 2(α) over Q, where t1, t2 are two different positive integers, and the numbers q ∈ Z � {0, ±1}, α ∈ Q � {0} are multiplicatively independent. Moreover, they also give the following result: Let I be any imaginary quadratic field and q ∈ ZI, |q |> 1. Suppose that t1,..., tl are pairwise different positive integers, and that the numbers α ∈ I � {0} are multiplicatively independent with q. Then the numbers 1, T q t k(α) (k = 1,..., l) are linear independent over I. Furthermore, if the numbers αk (k = 1,..., l) ∈ I � {0} are multiplicatively independent with q, then the numbers 1, T q t k(αk) (k = 1,..., l) are linear independent over I. Only outlines of the proofs are given

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.3914
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.