Let $F$ be a non-Archimedean locally compact field. Let $\sigma$ and $\tau$ be finite-dimensional representations of the Weil-Deligne group of $F$. We give strong upper and lower bounds for the Artin and Swan exponents of $\sigma\otimes\tau$ in terms of those of $\sigma$ and $\tau$. We give a different lower bound in terms of $\sigma\otimes\check\sigma$ and $\tau\otimes\check\tau$. Using the Langlands correspondence, we obtain the bounds for Rankin-Selberg exponents.
Bushnell, C. J., & Henniart, G. (2017). Strong exponent bounds for the local Rankin-Selberg convolution. Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), 143-167.
MLA
Colin J. Bushnell; G. Henniart. "Strong exponent bounds for the local Rankin-Selberg convolution", Bulletin of the Iranian Mathematical Society, 43, Issue 4 (Special Issue), 2017, 143-167.
HARVARD
Bushnell, C. J., Henniart, G. (2017). 'Strong exponent bounds for the local Rankin-Selberg convolution', Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), pp. 143-167.
VANCOUVER
Bushnell, C. J., Henniart, G. Strong exponent bounds for the local Rankin-Selberg convolution. Bulletin of the Iranian Mathematical Society, 2017; 43(Issue 4 (Special Issue)): 143-167.
