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Title of Journal: Isr J Math

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Abbravation: Israel Journal of Mathematics

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The Hebrew University Magnes Press

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DOI

10.1007/bf00840525

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1565-8511

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The unramified computation of RankinSelberg integ

Authors: Eyal Kaplan
Publish Date: 2011/12/05
Volume: 191, Issue: 1, Pages: 137-184
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Abstract

Let SO 2l be the special orthogonal group either split or quasisplit over a number field and 1 l n We compute the local integral where data are unramified derived from the global RankinSelberg construction for SO 2l × GL n In the general case the local integral is difficult to compute directly so instead it is transformed to an integral related to a construction for SO 2n+1×GL n which carries a Bessel model on SO 2n+1 For the quasisplit case when l = n − 1 we are able to compute the local integral by a modification of our recently introduced approach using invariant theory This leads to another proof of our result for 1 l n as well as a new proof of a known result regarding the unramified Bessel function

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  1. Characterizing stable complete Erdős space
  2. On prime ideals of noetherian skew power series rings
  3. Classification of quasifinite $$\mathcal{W}_\infty $$ -modules-modules
  4. Classification of quasifinite $$\mathcal{W}_\infty $$ -modules-modules
  5. De Rham theorem for Schwartz functions on Nash manifolds
  6. Random matrices and subexponential operator spaces
  7. An integral representation for topological pressure in terms of conditional probabilities
  8. Ribet bimodules and the specialization of Heegner points
  9. Maximally stable Gaussian partitions with discrete applications
  10. Extrinsic isoperimetry and compactification of minimal surfaces in Euclidean and hyperbolic spaces
  11. Homogeneity and local symmetry of complex ( κ , µ)-spaces
  12. Binary forms as sums of two squares and Châtelet surfaces
  13. On two Hamilton cycle problems in random graphs
  14. Derivatives for smooth representations of GL ( n , ℝ) and GL ( n , ℂ)
  15. Weak mixing and unique ergodicity on homogeneous spaces
  16. Invariant random subgroups of lamplighter groups
  17. Webb’s conjecture for fusion systems
  18. Partitions of nonzero elements of a finite field into pairs
  19. On typical properties of Hilbert space operators
  20. On a question of Sárközy on gaps of product sequences
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