Download Automorphic Forms and L-functions II: Local Aspects by David Ginzburg, Erez Lapid, David Soudry PDF

By David Ginzburg, Erez Lapid, David Soudry

This booklet is the second one of 2 volumes, which characterize prime topics of present study in automorphic varieties and illustration thought of reductive teams over neighborhood fields. Articles during this quantity customarily symbolize worldwide elements of automorphic types. one of the subject matters are the hint formulation; functoriality; representations of reductive teams over neighborhood fields; the relative hint formulation and sessions of automorphic types; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions. The articles are written by way of prime researchers within the box, and convey the reader, complex graduate scholars and researchers alike, to the frontline of the energetic study in those deep, important subject matters. The better half quantity (""Contemporary arithmetic, quantity 488"") is dedicated to international features of automorphic types

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Ibukiyama, On differential operators on automorphic forms and invariant pluriharmonic polynomials, Comm. Math. Univ. S. Pauli 48 (1999), 103-118. [IbuZ] T. Ibukiyama and D. Zagier, Invariant harmonic polynomials on polyspheres and some related differential equations, unfinished manuscript. [Kat97] H. Katsurada, An explicit formula for Siegel series, Amer. J. Math. 121 (1997), 415-452. [Kl67] H. Klingen, Zum Darstellungssatz f¨ ur Siegelsche Modulformen, Math. Z. 102 (1967), 30-43. [Kl90] H. Klingen, Introductory Lectures on Siegel Modular Forms, Cambridge University Press, 1990.

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9). 9); it does not depend on φ(. . . ) ⎧ 2n−1 3 ) if t11 ≡ t22 ≡ t33 ≡ 0(p2n−1 ) ⎨ (p 2πi·tr( p1n T aN pε Rv ) pn e = ⎩ 2n−1 0 otherwise ri mod p Remark. 5) of M that a · ε ≡ 1(p2n−1 ). Remark. This result is compatible with the expected “width” p. 9) av pn + aε N p2n−1 ” ” ·T . α, β, γ modN pn We decompose the summation into p-component and N -component: ε = N εp + p2n−1 εN 0 where εp = αp βp αp 0 γp βp γp 0 and αp , βp γp run modulo pn and analogously for εN . 10) a · {pn · u · 13 + εN }t ≡ 13 mod N p2n−1 .

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