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Showing 1 to 8 of 8 for “"Kloosterman Sums"”.
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Half-integral weight Kloosterman sums and integer partitions
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01
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Effective estimates for sums of Kloosterman sums, modular forms, and applications
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms
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Analytic and arithmetic applications of half integral weight automorphic forms
… integral weight Hecke theory to get bounds on sums of half integral weight Kloosterman sums. This is inspired by Sarnak and Tsimerman's treatment of weight zero Kloosterman sums in the context of the Linnik--Selberg conjecture. Each chapter is completely self contained and independent of the …
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Arithmetic of Maass forms of half-integral weight
… Next, we examine the deep relationship between sums of Kloosterman sums and Maass cusp forms, motivated by work of Kuznetsov and Sarnak-Tsimerman, among others. Finally, we focus on the classical mock theta functions of Ramanujan, and give a simple proof of the mock theta conjectures using the …
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On Some Applications of a Generalized Dwork Trace Formula to L-functions associated to Exponential Sums over Galois Rings
… trace formula that applies to exponential sums over Galois rings and the associated L-function. Using the generalized trace formula, we will prove more results on the L-function, analogous to the classical results by Dwork and Bombieri who studied L-functions associated to such exponential …
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Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory
… sequence with slope $s$. We also study partial sums of the form \begin{equation} \label{thabs1} \sum_{n\leq x} \frac{ a_{n+k}}{a_n} \end{equation} and find asymptotics for them. Next, we consider the series \begin{equation*} \sum_{n=1}^{\infty} \left(\frac{ a_{n+k}}{a_n}-\frac{ …
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Analytic and ergodic properties of certain classes of Euclidean algorithms
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms
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Topics in the theory of automorphic L-functions
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01