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FUNCTORIALITY FOR THE EXTERIOR SQUARE OF GL4 AND THE SYMMETRIC FOURTH OF GL2
Let ∧ : GLn(C) −→ GLN (C), where N = n(n−1) 2 , be the map given by the exterior square. Then Langlands’ functoriality predicts that there is a map from cuspidal representations of GLn to automorphic
Random matrices, Frobenius eigenvalues, and monodromy
Statements of the main results Reformulation of the main results Reduction steps in proving the main theorems Test functions Haar measure Tail estimates Large $N$ limits and Fredholm determinants
Zeroes of zeta functions and symmetry
Hilbert and Polya suggested that there might be a natural spectral interpretation of the zeroes of the Riemann Zeta function. While at the time there was little evidence for this, today the evidence
Ramanujan graphs
TLDR
The girth ofX is asymptotically ≧4/3 logk−1 ¦X¦ which gives larger girth than was previously known by explicit or non-explicit constructions.
The behaviour of eigenstates of arithmetic hyperbolic manifolds
In this paper we study some problems arising from the theory of Quantum Chaos, in the context of arithmetic hyperbolic manifolds. We show that there is no strong localization (“scarring”) onto
Chebyshev's Bias
TLDR
It is shown that the bias to the distribution to primes in ideal classes in number fields, and to prime geodesics in homology classes on hyperbolic surfaces, can be characterized exactly those moduli and residue classes for which the bias is present.
Extremals of determinants of Laplacians
On etudie le determinant associe au laplacien en fonction de la metrique sur une surface donnee et en particulier ses valeurs extremes quand la metrique est bien restreinte
Low lying zeros of families of L-functions
In Iwaniec-Sarnak [IS] the percentages of nonvanishing of central values of families of GL_2 automorphic L-functions was investigated. In this paper we examine the distribution of zeros which are at
Density of integer points on affine homogeneous varieties
(1.2) N(T, V)= {m V(Z): Ilmll T} where we denote by V(A), for any ring A, the set of A-points of V. Hence I1" is some Euclidean norm on R". The only general method available for such problems is the
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