automorphic form sentence in Hindi
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- Functoriality is the conjecture that automorphic forms on different groups should be related in terms of their-groups.
- Now suppose we are given a family of automorphic forms with a complex parameter " s ".
- Further, the automorphic forms for a given factor of automorphy correspond to sections of the corresponding line bundle.
- The theory is particularly well developed for symmetric spaces and provides a theory of automorphic forms ( discussed below ).
- This is almost possible and leads to a description of all automorphic forms in terms of these constructs and cusp forms.
- It requires the existence of an automorphic form, starting with an object that ( very abstractly ) lies in a category of motives.
- Automorphic forms are a generalization of modular forms to more general analytic functions, perhaps of several complex variables, with similar transformation properties.
- The Kuznetsov or " relative trace " formula connects Kloosterman sums at a deep level with the spectral theory of automorphic forms.
- Orbital integrals are an important technical tool in the theory of automorphic forms, where they enter into the formulation of various trace formulas.
- Modular forms are automorphic forms defined over the groups adelic approach as a way of dealing with the whole family of congruence subgroups at once.
- As a result, an entire philosophy, the Langlands program has developed around the relation between representation and number theoretic properties of automorphic forms.
- She was a speaker at the 1990 International Congress of Mathematicians, on decomposition into distinguished subspaces of certain spaces of square-integral automorphic forms.
- The theory of modular forms ( and, more generally, automorphic forms ) also occupies an increasingly central place in the toolbox of analytic number theory.
- Shimura himself has described his approach as'phenomenological': his interest is in finding new types of interesting behaviour in the theory of automorphic forms.
- This opened a field for later research on associated Dirichlet series and automorphic forms, and was a major step in the solution of Kummer's conjecture.
- "' Stephen S . Kudla "'( born 1950 Caracas, Venezuela ) is an American mathematician working in arithmetic geometry and automorphic forms.
- This is especially convenient in the theory of automorphic forms : for example all modern treatments of the Arthur-Selberg trace formula are done in this ad�lic setting.
- The values of " j " may be complex numbers, or in fact complex square matrices, corresponding to the possibility of vector-valued automorphic forms.
- Kra studies Riemann surfaces and their moduli spaces ( Teichm�ller spaces ) and their connection with Kleinian groups and associated automorphic forms and their applications for example in number theory.
- His research deals with arithmetic geometry, automorphic forms, Leibniz Prize by the Deutsche Forschungsgemeinschaft . In 2004 Harder received, with Friedhelm Waldhausen, the von Staudt Prize.
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