%0 Thesis %A Peters, Lloyd Christopher %D 2017 %T Non-commutative iwasawa theory for d-Fold false tate extensions %U https://bridges.monash.edu/articles/thesis/Non-commutative_iwasawa_theory_for_d-Fold_false_tate_extensions/4684399 %R 10.4225/03/58ae646d94556 %2 https://bridges.monash.edu/ndownloader/files/7642414 %K P-adic L-functions %K thesis(doctorate) %K Iwasawa theory %K 1959.1/965406 %K ethesis-20140627-123910 %K Open access %K 2014 %K Elliptic curves %K False tate extensions %K monash:128548 %X For the (d+1)-dimensional Lie group G=Z_p^{ imes}ltimes Z_p^{oplus d}, we determine through the use of p-power congruences, a necessary and sufficient set of conditions whereby a collection of abelian p-adic L-functions arises from an element in K_1(Z_p[[G]]). We construct an additive theta map which produces additive p-power congruences, and then using the Taylor Oliver logarithm, we arrive at a multiplicative version of these congruences. If E is a semistable elliptic curve over Q with good ordinary reduction at p, the abelian p-adic L-functions already exist, therefore one can predict many new families of higher order congruences. The first layer congruences are then verified computationally in a variety of cases. The final chapter contains computations for elliptic curves with bad multiplicative reduction at p, that the author performed for Delbourgo and Lei in [10]. All of the computations were done using the package MAGMA. %I Monash University