An ergodic value distribution of certain meromorphic functions

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• 作者：Junghun Lee up>m12003v@math.nagoya-u.ac.jp" class="auth_mail" title="E-mail the corresponding authorup> ; Ade Irma Suriajayaup> ; up>up>m12026a@math.nagoya-u.ac.jp" class="auth_mail" title="E-mail the corresponding authorup>
• 关键词：Lindel&ouml ; f hypothesis ; Birkhoff's ergodic theorem ; Zeta function ; L-function ; Derivative
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：125-138
• 全文大小：378 K

文摘

We calculate a certain mean-value of meromorphic functions by using specific ergodic transformations, which we call affine Boolean transformations. We use Birkhoff's ergodic theorem to transform the mean-value into a computable integral which allows us to completely determine the mean-value of this ergodic type. As examples, we introduce some applications to zeta functions and L-functions. We also prove an equivalence of the Lindelöf hypothesis of the Riemann zeta function in terms of its certain ergodic value distribution associated with affine Boolean transformations.