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Twists of a General Class of L-Functions by Highly Ramified Characters

Published online by Cambridge University Press:  20 November 2018

Freydoon Shahidi
Freydoon Shahidi*
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907, U.S.A. U.S.A., email: [email protected]
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Abstract

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It is shown that given a local $L$-function defined by Langlands-Shahidi method, there exists a highly ramified character of the group which when is twisted with the original representation leads to a trivial $L$-function.

Keywords

11F7022E3522E50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 3 , 01 September 2000 , pp. 380 - 384
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Jacquet, H. and Shalika, J. A., A lemma on highly ramified ε-factors. Math. Ann. 84 (1985), 319–332.Google Scholar
[2] Langlands, R. P., Euler Products. Yale Univ. Press, New Haven, Connecticut, 1971.Google Scholar
[3] Prasad, D. and Ramakrishnan, D., On the global root numbers of GL(n) × GL(m). To appear in Shimura's volume.Google Scholar
[4] Shahidi, F., On the Ramanujan conjecture and finiteness of poles for certain L-functions. Ann. of Math. 127 (1988), 547–584.Google Scholar
[5] Shahidi, F., A proof of Langlands’ conjecture on Plancherel measures: Complementary series for p-adic groups. Ann. of Math. 132 (1990), 273–330.Google Scholar
[6] Shahidi, F., On certain L-functions. Amer. J.Math. 103 (1981), 297–356.Google Scholar