Global ETD Search
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Showing 1 to 11 of 11 for “"L-series"”.
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Vanishing and non-vanishing of L-series of elliptic curves twisted by Dirichlet characters
We study the behaviour of L -series of elliptic curves twisted by Dirichlet characters. In particular, we study the vanishing and non vanishing of these L -series at the critical point. We present empirical results indicating the vanishing behaviour of cyclic twists of orders 3, 5, 7 and conductors …
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Ground Movements Around Model Tunnels in Sand (Settlements, Shield, Photogrammetry)
… dry sand. The test program was divided into four series of tests. In the O-, M-, and T-series, two concentrically placed circular tubes were used representing the model shield and model liner, respectively. The model shield was pulled out of the test bin in several steps and an annular gap between …
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Analytic and arithmetic applications of half integral weight automorphic forms
… of Hoffstein (2011) that asserts that the L-series attached to a half integral weight modular form satisfies a Lindelof hypothesis. Using spectral and diophantine techniques, the first chapter establishes a twisted second moment of L-series attached to such forms with a power saving error …
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Hypergeometric functions and Mahler measure
… and special values of different types of L-series. This thesis contains four papers which either prove or attempt to prove conjectures due to Boyd. The introductory chapter contains an overview of the contents of each manuscript.
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Topics on the Spectral Theory of Automorphic Forms
… study the analytic properties of the Eisenstein Series of $frac {1}{2}$-integral weight associated with the Hecke congruence subgroup $Gamma_0(4)$. Using these properties we obtain asymptotics for sums of certain Dirichlet $L$-series. We also obtain a formula reducing the study of Selberg's …
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Positivity properties associated with linear differential operators
… We prove our result using a generalized Taylor Series Expansion known as the L-series. The L-series expansion about t = t₀ for a function fƐC<sup>∞</sup> is: ∞ Σ Lᵏf(t₀)Φ<sub>2k</sub>(t) + √(a₂(t₀))(Lᵏf)' (t₀)Φ<sub>2k+1</sub>(t). k=0 The "L-basis" functions …
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Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula
… these representations fall into a principle series, indexed by characters on a torus of the metaplectic group, and there is an associated an L-function. In the final section of their paper, an equivalence is shown in the rank one case between this -function and an Dirichlet series defined …
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On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication
… integers of $K$. Let us assume the complex $L$-series $L(E/K,s)$ of $E$ over $K$ does not vanish at $s=1$. K. Rubin showed, using Iwasawa theory, that the $p$-part of Birch and Swinnerton-Dyer conjecture holds for $E$ for all prime numbers $p$ which do not divide the order of the group of roots …
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Chiral phosphonyl and thiophosphonyl carbanions in asymmetric alkylation and olefination reactions
A series of 3-substituted 2-benzyl-6-methyl-1,3,2-oxazaphosphorinane-2-oxides, derived from (S)-N-alkyl-4-amino-2-butanols, was prepared. The alkylation behavior of the derived lithium anions was examined as a function of the N-substituents and electrophiles. In the l-series, the methylation …
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Iwasawa theory for tensor products of Hilbert modular forms
… interpolates critical values of the complex L-series, and the Selmer group which is an important object used to control the growth of arithmetic data. In this thesis, we explore some questions that arise organically from the Iwasawa Main Conjecture, applied to Hilbert modular forms and their …
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ESD Protected SiGe HBT RFIC Power Amplifiers
… (DECT) applications. An on-chip shunt-L-series-C input matching network was used to provide ESD protection to the input pin of the DECT PA. A much more area efficient (as compared to the diode ring technique) Zener diode approach was used to protect the control and signal lines. The PA's …