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Why must functions in Selberg class be of finite order?

L函数 Math StackExchange 0 票 0 回答 2 浏览 提问者: bxhlywzzcr 2026-06-16 00:49
definition l-functions

问题内容

One of the axioms for Selberg class is that for some natural number $m$, $(s-1)^mF(s)$ extends to an entire function of finite order. What is the use of "finite order"? If we allow it to be of infinite order, what will happen?

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