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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.01512 |
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Table of Contents:
- Let $π$ be an irreducible cuspidal automorphic representation of $\text{GL}_n(\mathbb A_\mathbb Q)$ with associated $L$-function $L(s, π)$. We study the behaviour of the partial Euler product of $L(s, π)$ at the center of the critical strip. Under the assumption of the Generalized Riemann Hypothesis for $L(s, π)$ and assuming the Ramanujan--Petersson conjecture when necessary, we establish an asymptotic, off a set of finite logarithmic measure, for the partial Euler product at the central point that confirms a conjecture of Kurokawa. As an application, we obtain results towards Chebyshev's bias in the recently proposed framework of Aoki-Koyama.