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25 is a centered octagonal number, a centered square number, and an automorphic number.
como la suma de sus factores es 6 < 25, se trata de un número defectivo.

b. spectral theory of automorphic functions.
b. spectral theory of automorphic functions.

this function is an early example of an automorphic function and in this work schwarz was looking at ideas which led klein and poincaré to develop the theory of automorphic functions.
esta función es un temprano ejemplo de una función automorphic y en este trabajo schwarz estaba buscando a las ideas que llevaron klein y poincaré para desarrollar la teoría de funciones automorphic.

in fact the use of scattering theory for automorphic functions was studied by lax and phillips in scattering theory for automorphic functions (1976).
de hecho, el uso de la teoría de la dispersión de funciones automorphic fue estudiado por lax y phillips en la teoría de dispersión automorphic funciones (1976).

==references==* iwaniec, h. spectral methods of automorphic forms, american mathematical society, second edition, 2002.
* iwaniec, h. spectral methods of automorphic forms, american mathematical society, second edition, 2002.

isbn 0-387-97127-0* goro shimura, "introduction to the arithmetic theory of automorphic functions".
isbn 0-387-97127-0* gorō shimura: "introduction to the arithmetic theory of automorphic functions".

his first accomplishment in this field was a formula for the dimension of certain spaces of automorphic forms, in which particular types of harish-chandra's discrete series appeared.
su primer logro en este campo es una fórmula para la dimensión de determinados espacios de formas automórficas, en la que determinados tipos de harish-chandra de la serie parecían discretas.

they form one of the two major classes of global "l"-functions, the other being the "l"-functions associated to automorphic representations.
ellas forman una de las dos principales clases de funciones "l" globales, las otras son las funciones "l" asociadas a la representación automórfica.

== rise of the general theory ==this development preceded the langlands program by a few years, and can be regarded as complementary to it: langlands' work relates largely to artin "l"-functions, which, like hecke's "l"-functions, were defined several decades earlier, and to "l"-functions attached to general automorphic representations.
== rise of the general theory ==this development preceded the langlands program by a few years, and can be regarded as complementary to it: langlands' work relates largely to artin "l"-functions, which, like hecke's "l"-functions, were defined several decades earlier, and to "l"-functions attached to general automorphic representations.