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Some uniqueness results related to L-functions

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Abstract

In this paper, we describe a family of meromorphic functions in \(\mathbf {C}\) from analyzing some properties of these L-functions in the extended Selberg class and show two uniqueness results of such a function, in terms of shared values with a general meromorphic function in \(\mathbf {C}\). In particular, we show the condition “\(\displaystyle {1\mathsf{CM}+3\mathsf{IM}}\) value-sharing” suffices.

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Notes

  1. When \(\rho (f)=0\), we do not need to consider \(\tau (f)\) in view of the transcendentality of f.

  2. Recall when f has finite order, then S(rf) is \(\displaystyle {O\left( \log r\right) }\) as a straightforward consequence of the logarithmic derivative lemma.

  3. The same observation of \(\tau (f)\) as mentioned in Theorem 2.1 applies here when \(\rho (f)=0\).

  4. The same convention about \(\tau (f)\) as settled in theorems 2.1 and 3.2 applies here, and hereafter, if \(\rho (f)=0\).

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Correspondence to Qi Han.

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Dedicated to Professor Seiki Mori on the occasion of his 72nd birthday.

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Han, Q. Some uniqueness results related to L-functions. Boll Unione Mat Ital 10, 503–515 (2017). https://doi.org/10.1007/s40574-016-0081-1

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