Keijo O. Väänänen

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This paper considers rational integer values of Kloosterman sums over finite fields of characteristic <i>p</i> &gt; 3. We shall prove two main results. The first one is a congruence relation satisfied by possible integer values. One consequence is that there are no Kloosterman zeroes in the case of characteristic <i>p</i> &gt; 3, which generalizes recent(More)
We investigate arithmetic properties of values of the entire function F (z) = F q (z; λ) = ∞ n=0 z n n j=1 (q j − λ) , |q| > 1, λ / ∈ q Z>0 , that includes as special cases the Tschakaloff function (λ = 0) and the q-exponential function (λ = 1). In particular, we prove the non-quadraticity of the numbers F q (α; λ) for integral q, rational λ and α / ∈ −λq(More)
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