A note on the degree conjecture for the Selberg class |
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Authors: | Jerzy Kaczorowski Alberto Perelli |
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Affiliation: | (1) Faculty of Mathematics and Computer Science, A. Mickiewicz University, 61-614 Poznań, Poland;(2) Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italy |
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Abstract: | The degree conjecture for the Selberg class of L-functions states that the degree d F of every F ∈ is an integer. Moreover, it is expected that every F ∈ has polynomial Euler product, and that the degree ∂ F of such an Euler product coincides with d F . In this note we prove that a suitable continuity assumption on the degree d F implies that ∂ F = d F for all F ∈ with polynomial Euler product. |
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Keywords: | L-functions Selberg class degree conjecture polynomial Euler products |
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