A note on the degree conjecture for the Selberg class |
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| Authors: | Jerzy Kaczorowski Alberto Perelli |
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| Institution: | (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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