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The Second Moment of Rankin-Selberg L-functions, Hybrid Subconvexity Bounds, and Related Topics

Ye, Zhilin
http://rave.ohiolink.edu/etdc/view?acc_num=osu1405076835

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Mathematics.
In this thesis, we study three problems related to subconvexity bounds of Rankin-Selberg L-functions. Let M,N be two coprime square-free integers. Let f be either a holomorphic or a Maass cusp form of level N. Using a large sieve inequality, we establish a bound for an unamplified 2nd moment average, such as ∑ |L(1/2+it,f ⊗ g)|^2 << (M+M^{2/3-β}N^&007B;) 4/3})(MN)^{ε} where β ≈ 1/500 and the sum is over g ranges over an orthonormal basis of holomorphic cusp forms of level M and a fixed weight for any j. As a consequence, we obtain a subconvexity bound for L(1/2+it,f ⊗ g) for any N < M satisfying the conditions above. Moreover, by symmetry, we establish a level aspect hybrid subconvexity bound for any coprime square-free M and N when both forms are holomorphic. We also establish a sup-norm bound for holomorphic forms such that y^{k/2}f(z) << k^{1/2}N^{-1/6+ ε }||f||_2^{1/2}. Furthermore, we establish an equidistribution property of mod c reciprocals which is natural to the subconvexity problem and second moments of Rankin-Selberg L-functions.
Roman Holowinsky (Advisor)
Wenzhi Luo (Committee Member)
James Cogdell (Committee Member)
Mark Berliner (Committee Member)
136 p.
Mathematics

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Citations

  • Ye, Z. (2014). The Second Moment of Rankin-Selberg L-functions, Hybrid Subconvexity Bounds, and Related Topics [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1405076835

    APA Style (7th edition)

  • Ye, Zhilin. The Second Moment of Rankin-Selberg L-functions, Hybrid Subconvexity Bounds, and Related Topics. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1405076835.

    MLA Style (8th edition)

  • Ye, Zhilin. "The Second Moment of Rankin-Selberg L-functions, Hybrid Subconvexity Bounds, and Related Topics." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1405076835

    Chicago Manual of Style (17th edition)

osu1405076835
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This open access ETD is published by The Ohio State University and OhioLINK.