On the local Langlands conjecture forGL(2)

Tunnell, Jerrold B.

doi:10.1007/bf01393255

Cited by 65 publications

(44 citation statements)

References 13 publications

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“…1 ; 2 /, where 1 and 2 both have conductor dividing q n 1 . In any case, the central character " f;q has conductor dividing q n 1 (see [Tu1,Proposition 3.4]). We claim then that…”

Section: Proofmentioning

confidence: 99%

Generalized Heegner cycles and p-adic Rankin L-series

Bertolini¹,

Darmon²,

Prasanna³

2013

Duke Math. J.

143

320

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“…1 ; 2 /, where 1 and 2 both have conductor dividing q n 1 . In any case, the central character " f;q has conductor dividing q n 1 (see [Tu1,Proposition 3.4]). We claim then that…”

Section: Proofmentioning

confidence: 99%

Generalized Heegner cycles and p-adic Rankin L-series

Bertolini¹,

Darmon²,

Prasanna³

2013

Duke Math. J.

143

320

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“…For n=2 this conjecture was proven by Tunnell in [9], for (n,p)= 1 it follows from [5]. In the present paper we prove it for the case n =p.…”

Section: R(c)=r'(c) If C>pmentioning

confidence: 64%

On the local langlands conjecture for central division algebras of indexp

Koch¹

1980

Invent Math

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“…Let K 0 = F q ((T )) be the completion of K at v = 0. To E/K 0 there correspond an automorphic representation σ E of GL(2, K 0 ) and also a representation σ E of H * , where H/K 0 is the central division algebra of dimension 4 (see [5], [2], [13]). E being defined over K = F q (T ) and subject to (1.2), the sign w(E/K) is nothing else than the root number (e.g., [1], p. 22) of σ E .…”

Section: Commentsmentioning

confidence: 99%

Zeta functions of a class of elliptic curves over a rational function field of characteristic two

1999

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Abstract. We show how to calculate the zeta functions and the orders |X| of Tate-Shafarevich groups of the elliptic curves with equation Y 2 + XY = X 3 + αX 2 + const · T −k over the rational function field Fq(T ), where q is a power of 2. In the range q = 2, k ≤ 37, α ∈ F 2 [T −1 ] odd of degree ≤ 19, the largest values obtained for |X| are 47 2 (one case), 39 2 (one case) and 27 2 (three cases).We observe and discuss a remarkable pattern for the distributions of signs in the functional equation and of fudge factors at places of bad reduction. These imply strong restrictions on the precise form of the Langlands correspondence for GL(2) over local or global fields of characteristic two.

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On the local Langlands conjecture forGL(2)

Cited by 65 publications

References 13 publications

Generalized Heegner cycles and p-adic Rankin L-series

Generalized Heegner cycles and p-adic Rankin L-series

On the local langlands conjecture for central division algebras of indexp

Zeta functions of a class of elliptic curves over a rational function field of characteristic two

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