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Showing 1 to 20 of 45 for “"L-functions"”.
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L-functions in Number Theory
… 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 the connections between objects in different fields. Although most generalizations …
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L-functions and J-spectra
… have studied the twistings of the Riemann ζ-functions and Eisenstein series by Dirichlet characters. We first explain congruences of these twisted Eisenstein series of level Γ_1(N) and character χ via the Dieudonné theory of height 1 formal groups and formal A-modules and their finite …
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Extreme values of L-functions
Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2020-08-01
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Character Theory and Artin L-functions
… together with the Artin formalism to study L-functions in this thesis. One of the major themes is motivated by the work of Heilbronn and many others on classical Heilbronn characters. We define the arithmetic Heilbronn characters and apply them to study L-functions. In particular, we prove a …
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Moments Of Products Of L-Functions
… of the nontrivial zeros of certain Dedekind zeta-functions. In particular, let K be a quadratic number field. Using the mixed second moments of derivatives of the Dedekind zeta-function attached to K on the critical line, we prove the existence of gaps between consecutive zeros of the Dedekind …
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p-adic L-functions of automorphic forms
Let F be a number field, p a prime number. To an (adelic) automorphic representation of GL2 over F (with certain conditions 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 …
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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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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
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Zeros and moments of L-functions and applications
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms
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On Selmer groups and factoring p-adic L-functions
… into a product of two Kubota-Leopoldt p-adic L-functions. In 1982, Greenberg proved the corresponding result on the algebraic side involving classical Iwasawa modules, as predicted by the main conjectures for imaginary quadratic fields and Q. Our methods are inspired by this work of Greenberg. …
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On the Theory of Zeta-functions and L-functions
… some recent results regarding Hurwitz and Lerch functions, as well as Dirichlet's L-function. We have also investigated some fundamental concepts related to these functions and their universality properties. In addition, we also discuss different formulations and approaches to the proof of the …
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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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Limit Theorems for L-functions in Analytic Number Theory
… rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using an approximation for the logarithm of zeta given by Selberg.</p>
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p-adic L-functions and the Geometry of Hida Families
… of automorphic forms is how $p$-adic $L$-functions over eigenvarieties relate to the geometry of these eigenvarieties. In this talk we explain results in this vein for the ordinary part of the eigencurve (i.e. Hida families). We address how Taylor expansions of one variable $p$-adic …
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On the distribution of central values of Hecke L-functions
… as questions regarding the family of <em>L</em>-functions over Q associated to the archimedian characters<em> ψ (k)</em> =<em> k -it</em> at the center point 1/2. There are many families of characters besides those strictly of archimedean-type, especially as one expands their scope to proper …
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P-adic L-functions for elliptic curves over CM fields
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1983
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"Mixed joint universality for Dirichlet L-functions and Hurwitz type zeta-functions" /
… joint universality theorems for Dirichlet L-functions and Hurwitz type zeta-functions, i.e., theorems on simultaneous approximation of a collection of analytic functions by shifts of Dirichlet L-functions which have Euler's product over primes and by shifts of Hurwitz type zeta-functions …
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Bounds for the Spectral Mean Value of Central Values of L-functions
… of spectral mean value of Rankin-Selberg L-functions at s = 1/2, which is an analogue for Eisenstein series of X. Li's result for Hecke-Maass forms.
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