关于$p$ -稳定的椭圆型的范数（附Keith Conrad的附录）
On the norms of $p$-stabilized elliptic newforms (with an appendix by Keith Conrad)
摘要：
设$f \in S_κ(Γ_0(N))$是一个Hecke本征形，其本征值为$λ_f(p)$，其中素数$p$不整除$N$ .令$α_p$和$β_p$是满足$α_p + β_p = λ_f(p)$和$α_p β_p = p^{κ-1}$的复数。我们计算了$f_{p}^{α_p}(z) = f(z) - β_{p} f(pz)$的范数以及$U_p f$的范数，包括经典的和非经典的。我们使用这些结果以及一些收敛性质的欧拉产品定义的对称平方L-函数的$f$给出一个“本地”分解的Petersson规范的$f$。
英文摘要：
Let $f \in S_κ(Γ_0(N))$ be a Hecke eigenform at $p$ with eigenvalue $λ_f(p)$ for a prime $p$ not dividing $N$. Let $α_p$ and $β_p$ be complex numbers satisfying $α_p + β_p = λ_f(p)$ and $α_p β_p = p^{κ-1}$. We calculate the norm of $f_{p}^{α_p}(z) = f(z) - β_{p} f(pz)$ as well as the norm of $U_p f$, both classically and adelically. We use these results along with some convergence properties of the Euler product defining the symmetric square L-function of $f$ to give a `local' factorization of the Petersson norm of $f$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
