1999
DOI: 10.1215/s0012-7094-99-09619-9
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Critical values of the twisted tensor L-function in the imaginary quadratic case

Abstract: Eisenstein series at s = 0 is E-rational, we are led to the rationality result we seek (Theorem 1).There is an interesting computational complication that we must tackle along the way. In reality, each of the integral expressions contains an algebraic sum of Gamma factors. It is not a priori obvious that this sum does not vanish at s = 0, and that, for this reason, in the proof of Theorem 1, we are not dividing by zero! Though it seems quite difficult to establish this non-vanishing by direct computation we ar… Show more

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Cited by 21 publications
(78 citation statements)
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“…Combining this map and the isomorphism of Proposition with the action of SL 2false(double-struckCfalse) above allows us to define a left action of SL 2false(double-struckCfalse) on V2false(double-struckCfalse). An explicit check, contained in , shows that this action can be explicitly described as γ·PAB=P1false|afalse|2+false|cfalse|2()a¯c¯ca()AB,γ=abcd.…”
Section: Bianchi Modular Symbolsmentioning
confidence: 95%
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“…Combining this map and the isomorphism of Proposition with the action of SL 2false(double-struckCfalse) above allows us to define a left action of SL 2false(double-struckCfalse) on V2false(double-struckCfalse). An explicit check, contained in , shows that this action can be explicitly described as γ·PAB=P1false|afalse|2+false|cfalse|2()a¯c¯ca()AB,γ=abcd.…”
Section: Bianchi Modular Symbolsmentioning
confidence: 95%
“…A Bianchi modular form is an automorphic form for GL 2 over an imaginary quadratic field. Here, we give only a very brief description of the theory; more detailed descriptions are given by Bygott in (focusing on weight 2) and Ghate in (for higher weights). The basic definitions are given in Section 1.1, whilst Section 1.2 looks at the L‐function of a Bianchi modular form, giving an integral formula for the twisted L‐function.…”
Section: Bianchi Modular Formsmentioning
confidence: 99%
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