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FUNCTORIALITY FOR THE EXTERIOR SQUARE OF GL4 AND THE SYMMETRIC FOURTH OF GL2

- Henry H. Kim, D. Ramakrishnan, P. Sarnak
- Mathematics
- 2003

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… Expand

Zeros of principal $L$-functions and random matrix theory

- Z. Rudnick, P. Sarnak
- Mathematics
- 1 December 1996

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… Expand

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… Expand

Ramanujan graphs

- A. Lubotzky, R. Phillips, P. Sarnak
- Mathematics, Computer ScienceComb.
- 15 November 2017

TLDR

The behaviour of eigenstates of arithmetic hyperbolic manifolds

- Z. Rudnick, P. Sarnak
- Mathematics
- 1 March 1994

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… Expand

Chebyshev's Bias

- M. Rubinstein, P. Sarnak
- Mathematics, Computer ScienceExp. Math.
- 1994

TLDR

Extremals of determinants of Laplacians

- B. Osgood, R. Phillips, P. Sarnak
- Mathematics
- 1 September 1988

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

- H. Iwaniec, W. Luo, P. Sarnak
- Mathematics
- 19 January 1999

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… Expand

Density of integer points on affine homogeneous varieties

- W. Duke, Z. Rudnick, P. Sarnak
- Mathematics
- 1993

(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… Expand

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