JP Journal of Algebra, Number Theory and Applications
Volume 39, Issue 6, Pages 1003 - 1022
(December 2017) http://dx.doi.org/10.17654/NT039061003 |
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A DESCRIPTION OF A DRINFELD MODULE WITH CLASS NUMBER AND RANK 1
Victor Bautista-Ancona, Javier Diaz-Vargas, José Alejandro Lara RodrÃguez and Francisco X. Portillo-Bobadilla
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Abstract: We work out in detail the Drinfeld module over the ring
The example in question is one of the four examples that come from quadratic imaginary fields with class number and rank one.
We develop specific formulas for the coefficients and of the exponential and logarithmic functions and relate them with the product of all monic elements of A of degree k. On the Carlitz module, and coincide, but this is not true for general Drinfeld modules. On this example, we obtain a formula relating both invariants. We prove also using elementary methods a theorem due to Thakur that relate two different combinatorial symbols important in the analysis of solitons. |
Keywords and phrases: Drinfeld module, exponential and logarithmic functions. |
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