29,832 research outputs found
Liouville numbers, Liouville sets and Liouville fields
Following earlier work by E.Maillet 100 years ago, we introduce the
definition of a Liouville set, which extends the definition of a Liouville
number. We also define a Liouville field, which is a field generated by a
Liouville set. Any Liouville number belongs to a Liouville set S having the
power of continuum and such that the union of S with the rational number field
is a Liouville field.Comment: Proceedings of the American Mathematical Society, to appea
On Approximation constants for Liouville numbers
We investigate some Diophantine approximation constants related to the
simultaneous approximation of for
Liouville numbers . For a certain class of Liouville numbers including
the famous representative and numbers in the Cantor
set, we explicitly determine all approximation constants simultaneously for all
.Comment: 12 page
Liouville Numbers and Schanuel's Conjecture
In this paper, using an argument of P. Erdos, K. Alniacik and E. Saias, we
extend earlier results on Liouville numbers, due to P. Erdos, G.J. Rieger, W.
Schwarz, K. Alniacik, E. Saias, E.B. Burger. We also produce new results of
algebraic independence related with Liouville numbers and Schanuel's
Conjecture, in the framework of G delta-subsets.Comment: Archiv der Math., to appea
Bulk one-point function on disk in one-matrix model
We consider bulk correlation numbers on disk in one-matrix model. Using the
recently found so-called resonance transformation from the KdV to the Liouville
frame, we obtain an explicit expression for the bulk one-point function. The
result is consistent with the form of FZZ one-point function in the boundary
Liouville Field Theory.Comment: 8 page
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