Publication

The Subconvexity Problem For Gl(2)

Philippe Michel
2010
Journal Articles

Abstract

Generalizing and unifying prior results, we solve the subconvexity problem for the L-functions of GL(1) and GL(2) automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino-Ikeda.

Official source

https://infoscience.epfl.ch/entities/publication/7a15508c-11c3-4448-a9b7-ab601c7e94d8

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Philippe Michel
2010
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/7a15508c-11c3-4448-a9b7-ab601c7e94d8

About this result

Related concepts (12)

Automorphic form

In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms are holomorphic automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being the modular group, or one of its congruence subgroups; in this sense the theory of automorphic forms is an extension of the theory of modular forms.

Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).

L-function

In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An L-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an L-function via analytic continuation. The Riemann zeta function is an example of an L-function, and one important conjecture involving L-functions is the Riemann hypothesis and its generalization. The theory of L-functions has become a very substantial, and still largely conjectural, part of contemporary analytic number theory.

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