Zagier's conjecture on L ( E ,2)

Goncharov, A. B.; Levin, A.

doi:10.1007/s002220050228

Cited by 28 publications

(24 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is straightforward [3, 3.8.13] from the definition of q 2 that q 2 (D ⊕ T ) = q 2 (D) (3.29) whenever T is a torsion point of E. Since ker ψ ⊆ Tor(E), (3.29) assures that q 2 (D ⊕ S) = q 2 (D) (3.30) for every S ∈ ker ψ , and this proves that (1) implies (3). Obviously (3) implies (4). Finally, if ker ψ has n elements, it follows from (3.30) that…”

Section: Lemma 35 Let G Be An Abelian Group Tor(g) Its Torsion Submentioning

confidence: 88%

A new look at Jarvis' distribution formula

Ayala

2009

Journal of Number Theory

View full text Add to dashboard Cite

Section: Lemma 35 Let G Be An Abelian Group Tor(g) Its Torsion Submentioning

confidence: 88%

A new look at Jarvis' distribution formula

Ayala

2009

Journal of Number Theory

View full text Add to dashboard Cite

“…However, a similar functional relation for the elliptic Bloch-Wigner function and the construction of an elliptic analogue of the Bloch group has already been discussed in ref. [27]. In contrast to the genus-zero case, where the five-term identity suffices to represent a large class of functional identities of the dilogarithm, a whole class of functional identities given by eq.…”

Section: Genus Zeromentioning

confidence: 99%

Functional relations for elliptic polylogarithms

Broedel

Kaderli²

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Numerous examples of functional relations for multiple polylogarithms are known. For elliptic polylogarithms, however, tools for the exploration of functional relations are available, but only very few relations are identified. Starting from an approach of Zagier and Gangl, which in turn is based on considerations about an elliptic version of the Bloch group, we explore functional relations between elliptic polylogarithms and link them to the relations which can be derived using the elliptic symbol formalism. The elliptic symbol formalism in turn allows for an alternative proof of the validity of the elliptic Bloch relation. While the five-term identity is the prime example of a functional identity for multiple polylogarithms and implies many dilogarithm identities, the situation in the elliptic setup is more involved: there is no simple elliptic analogue, but rather a whole class of elliptic identities.

show abstract

“…Ces travaux ont permis à Goncharov et Levin de démontrer la conjecture de Zagier, reliant la valeur spéciale L(E, 2) associée à une courbe elliptique E définie sur Q, et la fonction dilogarithme elliptique [27], [14].…”

Section: Introductionunclassified

Valeur en $2$ de fonctions $L$ de formes modulaires de poids $2$ : théorème de Beilinson explicite

Brunault¹

2007

Bul. Soc. Math. France

View full text Add to dashboard Cite

Résumé. -Nous montrons une version explicite du théorème de Beilinson pour la courbe modulaire X 1 (N ). Ce résultat est la première étape d'un travail reliant, d'une part, la valeur en 2 de la fonction L d'une forme primitive de poids 2, et d'autre part, la fonction dilogarithme associée à la courbe modulaire correspondante, dans l'esprit de la conjecture de Zagier pour les courbes elliptiques. Comme corollaire de notre théorème, dans le cas où N est premier, nous répondons à une question de Schappacher et Scholl concernant l'image de l'application régulateur de Beilinson.Abstract (Value at 2 of L-functions of modular forms of weight 2: an explicit version of Beilinson's theorem)We prove an explicit version of Beilinson's theorem for the modular curve X 1 (N ). This result is the first step of a work linking the value at 2 of the L-function of a newform of weight 2 on the one hand, and the dilogarithm function associated to the corresponding modular curve on the other, in the spirit of Zagier's conjecture for elliptic curves. As a corollary of our theorem, in the case N is prime, we answer a question raised by Schappacher and Scholl concerning the image of Beilinson's regulator map. Texte reçu le 2 mars 2006, accepté le 15 mai 2006François Brunault,

show abstract

Zagier's conjecture on L ( E ,2)

Cited by 28 publications

References 20 publications

A new look at Jarvis' distribution formula

A new look at Jarvis' distribution formula

Functional relations for elliptic polylogarithms

Valeur en $2$ de fonctions $L$ de formes modulaires de poids $2$ : théorème de Beilinson explicite

Contact Info

Product

Resources

About