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Renormalized Periods on GL(3)

  • Jennifer Beineke (a1) and Daniel Bump (a2)

Abstract

A theory of renormalization of divergent integrals over torus periods on $\text{GL}\left( 3 \right)$ is given, based on a relative truncation. It is shown that the renormalized periods of Eisenstein series have unexpected functional equations.

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References

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[A] Arthur, J., A trace formula for reductive groups, I. Terms associated to classes in G(Q) . Duke Math. J. 45(1978), 911952.
[B] Bump, D., Automorphic Forms and Representations. Cambridge, 1997.
[BB] Bump, D. and Beineke, J., Hidden symmetries for a renormalized integral of Eisenstein series. Forum Math. 14(2002), 457475.
[BG] Bump, D. and Goldfeld, D., A Kronecker limit formula for cubic fields. In: Modular forms, (ed., Rankin, R.), 1984, 4349.
[GJ] Godement, R. and Jacquet, H., Zeta Functions of simple algebras. Springer Lecture Notes in Math. 260, 1972.
[JLR] Jacquet, H., Lapid, E. and Rogawski, J., Periods of automorphic forms. J. Amer.Math. Soc. 12(1999), 173240.
[K] Kudla, S., Seesaw dual reductive pairs. In: Automorphic forms of several variables, (eds., Satake, I. and Morita, Y.), Birkhäuser Progr. Math. 46, 1984, 244268.
[MW] Moeglin, C. and Waldspurger, J.-L., Spectral decomposition and Eisenstein series. Une paraphrase de l'Écriture, Cambridge, 1995.
[W] Woodson, J., The dual pair GL × GL. Stanford dissertation, (1994).
[Z] Zagier, D., The Rankin-Selberg method for automorphic functions which are not of rapid decay. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28(1981), 415437.
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Renormalized Periods on GL(3)

  • Jennifer Beineke (a1) and Daniel Bump (a2)

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