Catalogue


L-functions in Number Theory.
Zhang, Yichao.
imprint
2010.
description
91 leaves.
ISBN
9780494723548
format(s)
Microform, Thesis
Holdings
Subjects
subject term
More Details
imprint
2010.
isbn
9780494723548
restrictions
Electronic version licensed for access by U. of T. users.
dissertation note
Thesis (Ph.D.)--University of Toronto, 2010.
general note
Source: Dissertation Abstracts International, Volume: 72-07, Section: B, page: .
local note
ROBARTS MICROTEXT copy on microfiche.
abstract
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 the connections between objects in different fields. Although most generalizations are largely conjectural, there are many existing results that provide us the evidence.Finally, we consider the Artin L-functions attached to irreducible 4-dimensional S5-Galois representations and deal with the modularity problem. One sufficient condition on the modularity is given, which may help to find an affirmative example for Strong Artin Conjecture in this case.In this thesis, we shall consider some L-functions and look into some problems mentioned above. More explicitly, for the L-functions associated to newforms of fixed square-free level, we will consider an average version of the fourth moments problem. The final bound is proven by considering definite rational quaternion algebras and divisor functions in them, generalizing Maass Correspondence Theorem and one of Duke's results and eventually applying the solution to Basis Problem.We then consider the problem of expressing the central value at 1/2 of the Rankin-Selberg L-function associated to two newforms in terms of the Pertersson inner product, where one of the newforms is twisted by the derivative of some Eisenstein series.
catalogue key
7911237

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