An Experimental Approach to the Borwien Conjectures

Specialeforsvar ved Cathrine Sommer Jacobsen

Titel: An Experimental Approach to the Borwein Conjectures

  

Abstract: Based on the Borwein Conjectures, we examine various patterns in the signs of the terms produced by a finite product a form where we systematically skip certain powers for various primes. Even though we do not find any new primes for which this finite product produces a consistent periodic sign pattern as the ones presented in the Borwein Conjec-tures, we do find other significant sign patterns. Both in terms of the general sign distribu-tion and in terms of a pattern in at which term these sign pattern break. We find that when comparing the correct sign pattern found using the proof regarding the infinite product of the form above, then we see a correlation with the first terms. Furthermore, we see that by changing the definition of the sign of zero then we are able to find a consistent periodic sign pattern for p=2. Lastly, we carry out a computational verification of the first Borwein Conjecture for large values.

 

 

Vejledere: Søren Eilers, Henrik Laurberg Pedersen
Censor:      Christian Henriksen, DTU