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- Alexander Lubotzky, Ralph Phillips, Peter Sarnak
- Combinatorica
- 1988

- HENRY H. KIM, PETER SARNAK
- 2002

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 representations of GLN , which satisfies certain canonical properties. To explain, let F be a number field, and let A be its ring of adeles. Let π = ⊗ v πv be… (More)

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 is quite convincing. Firstly, there are the “function field” analogues, that is zeta functions of curves over finite fields and their generalizations. For these… (More)

- Alexander Lubotzky, Ralph Phillips, Peter Sarnak
- STOC
- 1986

Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to… (More)

In Iwaniec-Sarnak [IS] the percentages of nonvanishing of central values of families of GL2 automorphic L-functions was investigated. In this paper we examine the distribution of zeros which are at or near s = 1 2 (that is the central point) for such families of L-functions. Unlike [IS], most of the results in this paper are conditional, depending on the… (More)

(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 Hardy-Littlewood circle method, which however has certain limitations, requiring roughly that the codimension of V in the ambient space A", as well as the… (More)

- RAMANUJAN GRAPHS, GIULIANA DAVIDOFF, PETER SARNAK, ALAIN VALETTE
- 2003

Includes bibliographical references and index.

- Michael Rubinstein, Peter Sarnak
- Experimental Mathematics
- 1994

- Peter Sarnak
- 2003

These notes attempt to describe some aspects of the spectral theory of modular surfaces. They are by no means a complete survey.

- JEAN BOURGAIN, ALEX GAMBURD, PETER SARNAK
- 2008

This paper is concerned with the following general problem. For j = 1, 2, . . . , k let Aj be invertible integer coefficient polynomial maps of Z to Z (here n ≥ 1 and the inverses of Aj’s are assumed to be of the same type). Let Λ be the group generated by A1, . . . , Ak and let O = Ob = b · Λ be the orbit of some b ∈ Z under Λ. Given a polynomial f ∈ Q[x1,… (More)