Date of Award

2003

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Advisor

William Snyder

Second Committee Member

Henrik Bresinsky

Third Committee Member

Ali Ozluk

Abstract

The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).

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