ऑटोमॉर्फिक इसके अंग्रेजी अर्थ का उदाहरण

This case is used in the representation-theoretic approach to automorphic forms.

There are applications to mean values involving the Riemann zeta function, primes in short intervals, primes in arithmetic progressions, the spectral theory of automorphic functions and related topics.

The Kuznetsov or relative trace formula connects Kloosterman sums at a deep level with the spectral theory of automorphic forms.

The Kuznetsov trace formula was found by Kuznetsov while studying the growth of weight zero automorphic functions.

The local theta correspondence relates irreducible admissible representations over a local field, while the global theta correspondence relates irreducible automorphic representations over a global field.

Stephen Rallis showed a version of the global Howe duality conjecture for cuspidal automorphic representations over a global field, assuming the validity of the Howe duality conjecture for all local places.

Splitting of periods of automorphic forms.

A more recent use of Gelfand pairs is for splitting of periods of automorphic forms.

Let m be an automorphic form over G, then its H-period splits as a product of local factors (i.

Now suppose we are given a family of automorphic forms with a complex parameter"nbsp;s.

These collineations are called automorphic collineations.

If the dimension of a projective space P is at least two, every collineation of P is the composition of an automorphic collineation and a homography.

Also refer to automorphic for a type of symmetry where the digits (not just their positions) play a role in another type of symmetry.

Iwasawa–Tate theory was extended to the general linear group GL(n) over an algebraic number field and automorphic representations of its adelic group by Roger Godement and Hervé Jacquet in 1972 which formed the foundations of the Langlands correspondence.