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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the Poles of Rankin-Selberg Convolutions of Modular Forms
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by Xian-jin Li PDF
Trans. Amer. Math. Soc. 348 (1996), 1213-1234 Request permission

Abstract:

The Rankin-Selberg convolution is usually normalized by the multiplication of a zeta factor. One naturally expects that the non-normalized convolution will have poles where the zeta factor has zeros, and that these poles will have the same order as the zeros of the zeta factor. However, this will only happen if the normalized convolution does not vanish at the zeros of the zeta factor. In this paper, we prove that given any point inside the critical strip, which is not equal to $\frac {1}{2}$ and is not a zero of the Riemann zeta function, there exist infinitely many cusp forms whose normalized convolutions do not vanish at that point.
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Additional Information
  • Xian-jin Li
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Email: xianjin@math.purdue.edu
  • Received by editor(s): January 17, 1994
  • Received by editor(s) in revised form: April 13, 1995
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 1213-1234
  • MSC (1991): Primary 11M26, 11F11
  • DOI: https://doi.org/10.1090/S0002-9947-96-01540-1
  • MathSciNet review: 1333393