{"id":{"repo_id":"lethbridge","oai_identifier":"oai:opus.uleth.ca:10133/6103"},"canonical_url":"https://search.dev.ndltd.org/etd/lethbridge/oai:opus.uleth.ca:10133/6103","repository":{"repo_id":"lethbridge","name":"University of Lethbridge","base_url":"https://opus.uleth.ca/server/oai/request"},"display":{"title":"Moments and zeros of L-functions","abstract":"We study moments and zeros of L-functions in this thesis. In Chapter 2, by following closely Soundararajan-Young's method, we prove an asymptotic for the fourth moment of quadratic Dirichlet L-functions under the generalized Riemann hypothesis. Unconditionally, we are able to give a sharp lower bound that agrees with Keating-Snaith's conjecture. In Chapter 3, we use a recursive method that was pioneered by Heath-Brown and developed by Young to give an asymptotic with an error O(X1/2+E) for the smoothed first moment of quadratic twists of modular L-functions. The result is analogous to Sono's work on the second moment of quadratic Dirichlet L-functions. It improves previous results of Iwaniec and Soundararajan-Radziwill. In Chapter 4, we obtain an explicit result for the number of zeros, in a box, of Dedekind zeta functions, which improves a result of Trudgian. Our argument is based on previous works of Bennett-Martin-O'Bryant-Rechnitzer, Kadiri-Ng and Trudgian.","abstract_html":"We study moments and zeros of L-functions in this thesis. In Chapter 2, by following closely Soundararajan-Young's method, we prove an asymptotic for the fourth moment of quadratic Dirichlet L-functions under the generalized Riemann hypothesis. Unconditionally, we are able to give a sharp lower bound that agrees with Keating-Snaith's conjecture. In Chapter 3, we use a recursive method that was pioneered by Heath-Brown and developed by Young to give an asymptotic with an error O(X1/2+E) for the smoothed first moment of quadratic twists of modular L-functions. The result is analogous to Sono's work on the second moment of quadratic Dirichlet L-functions. It improves previous results of Iwaniec and Soundararajan-Radziwill. In Chapter 4, we obtain an explicit result for the number of zeros, in a box, of Dedekind zeta functions, which improves a result of Trudgian. Our argument is based on previous works of Bennett-Martin-O'Bryant-Rechnitzer, Kadiri-Ng and Trudgian.","abstract_has_math":false,"creators":["Shen, Quanli","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":"2026-07-27T20:02:17Z","subjects":["moments of L-functions","zeros of L-functions","Number theory","L-functions","Dissertations, Academic"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/6103"],"render_values":[{"text":"hdl:10133/6103","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":["moments of L-functions","zeros of L-functions","Number theory","L-functions","Dissertations, Academic"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["hdl:10133/6103"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.other","label":"Dc Description Other","values":["We study moments and zeros of L-functions in this thesis. In Chapter 2, by following closely Soundararajan-Young's method, we prove an asymptotic for the fourth moment of quadratic Dirichlet L-functions under the generalized Riemann hypothesis. Unconditionally, we are able to give a sharp lower bound that agrees with Keating-Snaith's conjecture. In Chapter 3, we use a recursive method that was pioneered by Heath-Brown and developed by Young to give an asymptotic with an error O(X1/2+E) for the smoothed first moment of quadratic twists of modular L-functions. The result is analogous to Sono's work on the second moment of quadratic Dirichlet L-functions. It improves previous results of Iwaniec and Soundararajan-Radziwill. In Chapter 4, we obtain an explicit result for the number of zeros, in a box, of Dedekind zeta functions, which improves a result of Trudgian. Our argument is based on previous works of Bennett-Martin-O'Bryant-Rechnitzer, Kadiri-Ng and Trudgian."]},{"key":"dc:title","label":"Title","values":["Moments and zeros of L-functions"]}]}],"canonical_facts":{"dc:date.issued":["2021"],"dc:description.other":["We study moments and zeros of L-functions in this thesis. In Chapter 2, by following closely Soundararajan-Young's method, we prove an asymptotic for the fourth moment of quadratic Dirichlet L-functions under the generalized Riemann hypothesis. Unconditionally, we are able to give a sharp lower bound that agrees with Keating-Snaith's conjecture. In Chapter 3, we use a recursive method that was pioneered by Heath-Brown and developed by Young to give an asymptotic with an error O(X1/2+E) for the smoothed first moment of quadratic twists of modular L-functions. The result is analogous to Sono's work on the second moment of quadratic Dirichlet L-functions. It improves previous results of Iwaniec and Soundararajan-Radziwill. In Chapter 4, we obtain an explicit result for the number of zeros, in a box, of Dedekind zeta functions, which improves a result of Trudgian. Our argument is based on previous works of Bennett-Martin-O'Bryant-Rechnitzer, Kadiri-Ng and Trudgian."],"dc:identifier":["hdl:10133/6103"],"dc:subject":["moments of L-functions","zeros of L-functions","Number theory","L-functions","Dissertations, Academic"],"dc:title":["Moments and zeros of L-functions"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T20:02:17Z"}