Title: Arithmetic on hyperelliptic Jacobians and singular curves
Abstract: Mumford representation encodes each divisor class in the Jacobian of a nonsingular hyperelliptic curve as a unique pair of polynomials. And Cantor’s Algorithm provides an implementation of the addition of two divisor classes in this setting. In my thesis, I extended these ideas to study the arithmetic on Jacobians of…
Title: Admmissible sets for Erdos sieves
Abstract: When considering a set of pairwise coprime numbers b_1,b_2,... the admissible sets, those which don't contain every congruence class mod b_i for any i, correspond to the closure of the shift {F+n} with n an integer and F those numbers not divisible by any b_i. When considering a generalization for Erdos sieves, this does not hold anymore. In this…
Title: Linear Disjointness, Relativised Cyclotomic Polynomials and Inflated G-extensions for Number Fields
Abstract: There had been many attempts to generalize cyclotomic polynomials by many authors: combinatorialapproach using MOebius Inversion, Number-Theoretic approacj=h by focussing on unitary divisors etc. Our approach takes the factorization of X^n-1 as the model and defines cyclotomic…
