We'll take a little tour of some famous and less famous integer recurrence sequences, including the Fibonacci numbers and elliptic divisibility sequences, viewing them as shadows of geometric group laws on curves, which connects these sequences to current topics in research. Along the way, we'll use software to visually explore some of their properties.
The integer shadows of curves
Oct. 13, 2020 1pm (Zoom)
Stefano Fiovaranti (JKU Linz, Austria)
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We investigate finitary functions from Z_n to Z_n for a squarefree number n. We show that for squarefree n the lattice of all clones on Z_n which contain the addition of Z_n is finite and we provide an upper bound for the cardinality of this lattice. Furthermore, we prove that these clones can be generated by functions of arity at most the greatest prime factor of n.