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Showing 1 to 20 of 28 for “"L-function"”.
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On Selmer groups and factoring p-adic L-functions
… of a 3-variable Rankin-Selberg p-adic L-function as a product of a 2-variable p-adic L-function related to the adjoint representation of a Hida family and a Kubota-Leopoldt p-adic L-function. We prove a result involving Selmer groups that along with Dasgupta's result is consistent with …
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p-adic L-functions of automorphic forms
… at places above p and ∞) we construct a p-adic L-function which interpolates the complex (Jacquet-Langlands) L-function at the central critical point. This is a generalization of a construction by Spieß over totally real fields. It seems well-suited to generalize his proof of the exceptional zero …
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Self-intersection of Manin-Drinfeld Cycles and Taylor expansion of L-functions
… theory is that higher central derivatives of L-functions of automorphic forms should correspond to the intersection numbers of special cycles on moduli spaces. A classic early result along this philosophy was achieved by Gross and Zagier, who proved that the derivative of the L-function of an …
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L-functions of twisted elliptic curves over function fields
… and computationally, elliptic curves and their L-functions over number fields, in particular over the rational numbers. Much less work has been done over function fields, especially computationally, where the underlying geometry of the function field plays an intimate role in the arithmetic of …
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On Some Applications of a Generalized Dwork Trace Formula to L-functions associated to Exponential Sums over Galois Rings
… celebrated proof of the rationality of the zeta function of an (affine or projective) algebraic variety over a finite field. In this thesis, we will prove a generalization of Dwork’s trace formula that applies to exponential sums over Galois rings and the associated L-function. Using the …
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L-functions in Number Theory
As a generalization of the Riemann zeta function, L-function has become one of the central objects in Number Theory. The theory of L-functions, which produces a large family of consequences and conjectures in a unified way, concerns their zeros and poles, functional equations, special values and …
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Singular theta lifts and near-central special values of Rankin-Selberg L-functions
… of weight 2 on a Shimura curve over Q against a function on the curve with logarithmic singularities at CM points obtained as a Borcherds lift. We prove a formula relating periods of this type to a near-central special value of a Rankin-Selberg L-function. The results provide evidence for …
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Iwasawa theory for tensor products of Hilbert modular forms
… provides a deep connection between the p-adic L-function which 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 …
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Boundary Value Problems Of Spaces Of Automorphic Forms
… − 1) for s in a subset of on-line zeros of an L-function, appearing as a compact period of cuspidal-data Eisenstein series on GL 4 . These ideas have their origins in re- sults of Hejhal and Colin de Verdi ́ere. In parallel with the GL(2) case, the corresponding pair-correlation and …
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Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions
… period integral to the central value of an L-function attached to the representation. In this thesis, using a relative trace formula approach, we prove the global twisted GGP conjecture in the unramified case, under some additional local assumptions on the quadratic extension and the …
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p-adic Heights of Heegner points on Shimura curves
… construction of the p-adic Rankin-Selberg L-function L_p(f_E,-) and prove that when the sign of its functional equation is -1, its central derivative is given by the p-adic height of a Heegner point on the abelian variety A associated to f. This p-adic Gross-Zagier formula generalises the …
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Zeros of P-Adic L-Functions and Densities Relating to Bernoulli Numbers
… it is known that the corresponding p-adic L-function L(,p)(s,(chi)(,i)) of Kubota and Leopoldt has a unique zero ('i)(kappa) in the p-adic integers. For every irregular pair (p,i) with p < 1000, several p-adic places of ('i)(kappa) are calculated using a p-adic Newton's method and the formula …
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Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula
… 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 using Gauss sums, in order to demonstrate the arithmetic content. In this paper we reexamine this …
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On the Theory of Zeta-functions and L-functions
… a body of knowledge that concerns Riemann zeta-function and its generalizations in a cohesive manner. In particular, we have studied and mentioned some recent results regarding Hurwitz and Lerch functions, as well as Dirichlet's L-function. We have also investigated some fundamental concepts …
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The Birch and Swinnerton-Dyer Conjecture for elliptic curves
… Swinnerton-Dyer Conjecture. After defining the L-function, we state the Birch and Swinnerton-Dyer Conjecture and discuss results which have been proved and some consequences. We discuss numerical verification of the Conjecture, and show some computations, including an example of our own.
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F-virtual Abelian Varieties and Rallis Inner Product Formula
… With this we can compute the pairing of theta functions and show in this case that it is related to the central value of Langlands L-function. This new case of Rallis inner product formula enables us to relate nonvanishing of L-value to the nonvanishing of theta lifting.
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Topics in analytic number theory
… where summation is over the zeros of an $L$-function attached to an automorphic representation. Conditionally on strong bounds on autocorrelations of the coefficients of $L$-functions, a corollary of our results is that the gaps between consecutive zeros of the Riemann zeta function are …
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Distribution of sequences related to L-functions
… of linear combinations of derivatives of $L$-functions. We consider a collection of such combinations and prove asymptotic formulas for the supremum of the real parts of their zeros. Moreover, an investigation of an inverse-type question related to the case of the Riemann zeta function is …
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Concentration and dispersion of primary care physicians and implications for access to care in Cook County, Illinois: 2000-2008
… methods such as kernel density mapping and the L-function are used to analyze changes in the spatial clustering and dispersion of primary care physician locations. Geographically weighted regression models are then used to compare primary care physician supply to the socioeconomic demographics of …
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Analytic and arithmetic applications of half integral weight automorphic forms
… of Ramanujan's famous third order mock theta function. We also prove a conjecture of Andrews (1966) relating to the convergence of said formula. The third chapter uses spectral techniques and half integral weight Hecke theory to get bounds on sums of half integral weight Kloosterman sums. This …
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