In this work we prove the local multiplicity at most one theorem underlying the definition and th... more In this work we prove the local multiplicity at most one theorem underlying the definition and theory of local γ-, ϵ- and L-factors, defined by virtue of the generalized doubling method, over any local field of characteristic 0. We also present two applications: one to the existence of local factors for genuine representations of covering groups, the other to the global unfolding argument of the doubling integral.
Let π be a simple supercuspidal representation of the symplectic group Sp 2l (F), over a p-adic f... more Let π be a simple supercuspidal representation of the symplectic group Sp 2l (F), over a p-adic field F. In this work, we explicitly compute the Rankin-Selberg γ-factor of rank-1 twists of π. We then completely determine the Langlands parameter of π, if p = 2. In the case that F = Q 2 , we give a conjectural description of the functorial lift of π, with which, using a recent work of Bushnell and Henniart, one can obtain its Langlands parameter.
We present an integral representation for the tensor product L-function of a pair of automorphic ... more We present an integral representation for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and local) model, which generalizes the Whittaker model. Here we consider linear groups, but our construction also extends to arbitrary degree metaplectic coverings; this will be the topic of an upcoming work.
Electronic Colloquium on Computational Complexity, 2006
Constructions of k-wise almost independent permutations have been receiving a growing amount of a... more Constructions of k-wise almost independent permutations have been receiving a growing amount of attention in recent years. However, unlike the case of k-wise independent functions, the size of previously constructed families of such permutations is far from optimal. This paper gives a new method for reducing the size of families given by previous constructions. Our method relies on pseudorandom generators for space-bounded computations. In fact, all we need is a generator, that produces "pseudorandom walks" on undirected graphs with a consistent labelling. One such generator is implied by Reingold's log-space algorithm for undirected connectivity . We obtain families of k-wise almost independent permutations, with an optimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most δ, then the size of the description of a permutation in the family is O(kn + log 1 δ ). * A preliminary version of this paper appeared in Random 2005. † Tel-Aviv University.
Constructions of k-wise almost independent permutations have been receiving a growing amount of a... more Constructions of k-wise almost independent permutations have been receiving a growing amount of attention in recent years. However, unlike the case of k-wise independent functions, the size of previously constructed families of such permutations is far from optimal. This paper gives a new method for reducing the size of families given by previous constructions. Our method relies on pseudorandom generators for space-bounded computations. In fact, all we need is a generator, that produces “pseudorandom walks” on undirected graphs with a consistent labelling. One such generator is implied by Reingold’s log-space algorithm for undirected connectivity [21,22]. We obtain families of k-wise almost independent permutations, with an optimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most δ, then the size of the description of a permutation in the family is $O(kn +\log \frac 1 {\delta})$ .
In this work we prove the local multiplicity at most one theorem underlying the definition and th... more In this work we prove the local multiplicity at most one theorem underlying the definition and theory of local γ-, ϵ- and L-factors, defined by virtue of the generalized doubling method, over any local field of characteristic 0. We also present two applications: one to the existence of local factors for genuine representations of covering groups, the other to the global unfolding argument of the doubling integral.
Let π be a simple supercuspidal representation of the symplectic group Sp 2l (F), over a p-adic f... more Let π be a simple supercuspidal representation of the symplectic group Sp 2l (F), over a p-adic field F. In this work, we explicitly compute the Rankin-Selberg γ-factor of rank-1 twists of π. We then completely determine the Langlands parameter of π, if p = 2. In the case that F = Q 2 , we give a conjectural description of the functorial lift of π, with which, using a recent work of Bushnell and Henniart, one can obtain its Langlands parameter.
We present an integral representation for the tensor product L-function of a pair of automorphic ... more We present an integral representation for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and local) model, which generalizes the Whittaker model. Here we consider linear groups, but our construction also extends to arbitrary degree metaplectic coverings; this will be the topic of an upcoming work.
Electronic Colloquium on Computational Complexity, 2006
Constructions of k-wise almost independent permutations have been receiving a growing amount of a... more Constructions of k-wise almost independent permutations have been receiving a growing amount of attention in recent years. However, unlike the case of k-wise independent functions, the size of previously constructed families of such permutations is far from optimal. This paper gives a new method for reducing the size of families given by previous constructions. Our method relies on pseudorandom generators for space-bounded computations. In fact, all we need is a generator, that produces "pseudorandom walks" on undirected graphs with a consistent labelling. One such generator is implied by Reingold's log-space algorithm for undirected connectivity . We obtain families of k-wise almost independent permutations, with an optimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most δ, then the size of the description of a permutation in the family is O(kn + log 1 δ ). * A preliminary version of this paper appeared in Random 2005. † Tel-Aviv University.
Constructions of k-wise almost independent permutations have been receiving a growing amount of a... more Constructions of k-wise almost independent permutations have been receiving a growing amount of attention in recent years. However, unlike the case of k-wise independent functions, the size of previously constructed families of such permutations is far from optimal. This paper gives a new method for reducing the size of families given by previous constructions. Our method relies on pseudorandom generators for space-bounded computations. In fact, all we need is a generator, that produces “pseudorandom walks” on undirected graphs with a consistent labelling. One such generator is implied by Reingold’s log-space algorithm for undirected connectivity [21,22]. We obtain families of k-wise almost independent permutations, with an optimal description length, up to a constant factor. More precisely, if the distance from uniform for any k tuple should be at most δ, then the size of the description of a permutation in the family is $O(kn +\log \frac 1 {\delta})$ .
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Papers by Eyal Kaplan