2026-09-19T17:59:25.939976900Zhttps://opus.uleth.ca/server/oai/request
oai:opus.uleth.ca:10133/61032021-12-07T07:04:57Zcom_10133_3346com_10133_1com_10133_296col_10133_3347col_10133_298
ULethbridge OPUS Repository supervisor Kadiri, Habiba supervisor Ng, Nathan author Shen, Quanli author University of Lethbridge. Faculty of Arts and Science 2021-12-06T21:33:50Z 2021-12-06T21:33:50Z 2021 https://hdl.handle.net/10133/6103 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. en_US moments of L-functions zeros of L-functions Number theory L-functions Dissertations, Academic Moments and zeros of L-functions Thesis 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