{"id":{"repo_id":"lethbridge","oai_identifier":"oai:opus.uleth.ca:10133/6100"},"canonical_url":"https://search.dev.ndltd.org/etd/lethbridge/oai:opus.uleth.ca:10133/6100","repository":{"repo_id":"lethbridge","name":"University of Lethbridge","base_url":"https://opus.uleth.ca/server/oai/request"},"display":{"title":"The correction factor in Artin type problems","abstract":"In 1927, Emil Artin conjectured a product expression for the density of primes p for which a given non-zero integer a is a primitive root modulo p. The conjectured density was proved in 1967 by Hooley under the assumption of the Generalized Riemann Hypothesis. In 2014, Lenstra, Moree, and Stevenhagen introduced a method involving character sums to deduce the formula for the product in the density for Artin’s conjecture. The method applies in similar problems such as the density of primes of cyclic reduction for Serre curves. In this thesis, we introduce a generalization of this method which yields product expressions for a large family of problems that can be stated by summations involving the orders of certain finite groups. As a consequence, the product expressions of some Artin type problems, such as the Titchmarsh Divisor Problem in Kummer families for primes in a given arithmetic progression, are computed here.","abstract_html":"In 1927, Emil Artin conjectured a product expression for the density of primes p for which a given non-zero integer a is a primitive root modulo p. The conjectured density was proved in 1967 by Hooley under the assumption of the Generalized Riemann Hypothesis. In 2014, Lenstra, Moree, and Stevenhagen introduced a method involving character sums to deduce the formula for the product in the density for Artin’s conjecture. The method applies in similar problems such as the density of primes of cyclic reduction for Serre curves. In this thesis, we introduce a generalization of this method which yields product expressions for a large family of problems that can be stated by summations involving the orders of certain finite groups. As a consequence, the product expressions of some Artin type problems, such as the Titchmarsh Divisor Problem in Kummer families for primes in a given arithmetic progression, are computed here.","abstract_has_math":false,"creators":["Fakhari, Milad","University of Lethbridge. Faculty of Arts and Science"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021","date_published":"2021","updated_at":"2026-07-27T20:02:11Z","subjects":["number theory","character sums method","density theorems","primes in congruence classes","algebraic number theory","Numbers, Prime","Dissertations, Academic"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/6100"],"render_values":[{"text":"hdl:10133/6100","href":null,"code":true}]}]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2021"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["number theory","character sums method","density theorems","primes in congruence classes","algebraic number theory","Numbers, Prime","Dissertations, Academic"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/6100"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["In 1927, Emil Artin conjectured a product expression for the density of primes p for which a given non-zero integer a is a primitive root modulo p. The conjectured density was proved in 1967 by Hooley under the assumption of the Generalized Riemann Hypothesis. In 2014, Lenstra, Moree, and Stevenhagen introduced a method involving character sums to deduce the formula for the product in the density for Artin’s conjecture. The method applies in similar problems such as the density of primes of cyclic reduction for Serre curves. In this thesis, we introduce a generalization of this method which yields product expressions for a large family of problems that can be stated by summations involving the orders of certain finite groups. As a consequence, the product expressions of some Artin type problems, such as the Titchmarsh Divisor Problem in Kummer families for primes in a given arithmetic progression, are computed here."]},{"key":"dc:title","label":"Title","values":["The correction factor in Artin type problems"]}]}],"canonical_facts":{"dc:date.issued":["2021"],"dc:description.other":["In 1927, Emil Artin conjectured a product expression for the density of primes p for which a given non-zero integer a is a primitive root modulo p. The conjectured density was proved in 1967 by Hooley under the assumption of the Generalized Riemann Hypothesis. In 2014, Lenstra, Moree, and Stevenhagen introduced a method involving character sums to deduce the formula for the product in the density for Artin’s conjecture. The method applies in similar problems such as the density of primes of cyclic reduction for Serre curves. In this thesis, we introduce a generalization of this method which yields product expressions for a large family of problems that can be stated by summations involving the orders of certain finite groups. As a consequence, the product expressions of some Artin type problems, such as the Titchmarsh Divisor Problem in Kummer families for primes in a given arithmetic progression, are computed here."],"dc:identifier":["hdl:10133/6100"],"dc:subject":["number theory","character sums method","density theorems","primes in congruence classes","algebraic number theory","Numbers, Prime","Dissertations, Academic"],"dc:title":["The correction factor in Artin type problems"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T20:02:11Z"}