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EnglishWe give a complete characterization of the solutions $F(s)$ of the analog in the Selberg class of Hecke's functional equation of conductor 5, namely [ left(rac{sqrt{5}}{2pi} ight)^s Gamma(s+mu) F(s) = omega left(rac{sqrt{5}}{2pi} ight)^{1-s} Gamma(1-s+overline{mu}) overline{F(1-overline{s})} ] with $Re{mu}geq 0$ and $|omega|=1$. The proof is based on several results from our theory of nonlinear twists of $L$-functions, applied to obtain a full description of the Euler factor of $F(s)$ at $p=2$, and then on some ideas from a 1995 paper by J.B.Conrey and D.W.Farmer on converse theorems for Euler products.
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| Titolo: | On a Hecke-type functional equation with conductor q=5 | |
| Autori: | ||
| Data di pubblicazione: | 2018 | |
| Rivista: | ||
| Abstract: | We give a complete characterization of the solutions $F(s)$ of the analog in the Selberg class of Hecke's functional equation of conductor 5, namely [ left(rac{sqrt{5}}{2pi} ight)^s Gamma(s+mu) F(s) = omega left(rac{sqrt{5}}{2pi} ight)^{1-s} Gamma(1-s+overline{mu}) overline{F(1-overline{s})} ] with $Re{mu}geq 0$ and $|omega|=1$. The proof is based on several results from our theory of nonlinear twists of $L$-functions, applied to obtain a full description of the Euler factor of $F(s)$ at $p=2$, and then on some ideas from a 1995 paper by J.B.Conrey and D.W.Farmer on converse theorems for Euler products. | |
| Handle: | http://hdl.handle.net/11567/913944 | |
| Appare nelle tipologie: | 01.01 - Articolo su rivista |
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