Lower bounds for Rankin–Selberg $L$-functions on the edge of the critical strip

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Abstract: Let

F

be a number field, and let

p i_{1}

and

p i_{2}

be distinct unitary cuspidal automorphic representations of

o p e r a t o r n a m e {G L}_{n_{1}} (m a t h b b A_{F})

and

o p e r a t o r n a m e {G L}_{n_{2}} (m a t h b b A_{F})

respectively. In this paper, we derive new lower bounds for the Rankin-Selberg

L

-function

L (s, p i_{1} i m e s w i d e t i l d e {p i}_{2})

along the edge

R e s = 1

of the critical strip in the

t

-aspect. The corresponding zero-free region for

L (s, p i_{1} i m e s w i d e t i l d e {p i}_{2})

is also determined.

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