Poziv na predavanje na engleskom jeziku An Algorithmic Approach to Cyclotomic Units

Odjel za matematiku Sveučilišta Josipa Jurja Strossmayera u Osijeku organizira predavanje An Algorithmic Approach to Cyclotomic Units, na engleskom jeziku

NAJAVA – Predavanje će se održati u četvrtak, 31. ožujka 2016. godine s početkom u 17 sati u predavaonici broj 36 na Odjelu za matematiku Sveučilišta Josipa Jurja Strossmayera u Osijeku (Trg Ljudevita Gaja 6).

Predavanje će održati:

• Dr. Marc Conrad, Assistant Professor, Department of Computer Science & Technology, University of Bedfordshire, Luton, UK

For ∈Nand (, ) = 1 let  := be a primitive th unit root. We define the group of cyclotomic numbers as the multiplicative group generated by elements of the form 1 − with k  0 mod . The group of cyclotomic units is defined as :=Z∩. It is well known that the group of cyclotomic units is of finite index within the full unit group Zof the cyclotomic extension Q. We extend the definitions above allowing  =  with  := and :=  respectively.

We investigate various aspects of multiplicative relations within  and  for ∈N. This leads to a geometrical interpretation and visualization of these relations. Of particular interest are the so-called “Ennola” relations that occur when  is of the form 4 or  where ,  and  are odd primes (with  = 60 and  = 105 being the smallest examples). We give explicit algorithms that construct these Ennola relations, determine a basis of both and and (recursively) calculate the basis representation of an arbitrary cyclotomic unit or number.