We introduce the L-function of an elliptic curve E over a number field and derive its elementary convergence properties. An L-function of this type was first introduced by Hasse, and the concept was greatly extended by Weil. For this reason it is frequently called the Hasse-Weil L-function...
We introduce an analog of the $L$-function for noncommutative tori. It is proved that such a function coincides with the Hasse-Weil $L$-function of an elliptic curve with complex multiplication. As a corollary, one gets a localization formula for polynomial rings in terms of the $K$-theory...
The local root number of elliptic curves with wild ramification Let E be an elliptic curve over a number field F. The root number is conjecturally the sign of the functional equation of L-function of E/F. It is defined ... Shin-ichi,Kobayashi - 《Mathematische Annalen》 被引量: 40发表...
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whereL_{C_{D}}(z)is the numerator of the zeta function associated to the hyperelliptic curve given in the affine form by \begin{aligned} C_{D} : y^{2}=D(T). \end{aligned} (2.6) The following proposition is quoted from Rudnick [17], and it is proved by using the explicit for...
Congruences on the L-Function of an Elliptic Curve Parametrised by Modular FunctionsThe author proves an algebraicity theorem for the periods of parabolic forms of any weight for the full modular group, gives explicit formulas for the coefficients of the forms, and constructs -adic analogs of ...
Let $F$ be a function field of characteristic $p>0$, $\\F/F$ a Galois extension with $Gal(\\F/F)\\simeq \\Z_l^d$ (for some prime $leq p$) and $E/F$ a non-isotrivial elliptic curve. We study the behaviour of Selmer groups $Sel_E(L)_r$ ($r$ any prime) as $L$ va...
Moments of quadratic twists of elliptic curve L-functions over function fieldsdoi:10.2140/ant.2020.14.1853Alexandra FloreaEdva Roditty-GershonH. M. BuiJonathan P. Keating
L-function and rational points on an elliptic curve via the classical number theory.doi:10.1089/hyb.2005.24.283Kazuma MoritaHybridomaCho-Ngwa, F., Daggfeldt, A., Titanji, V. P., & Gronvik, K. O. (2005). Preparation and characterization of specific monoclonal antibodies for the detection...
elliptic curveL-functionrankfinite fieldcorrelationWe calculate the first and second moments of L-functions in the family of quadratic twists of a fixed elliptic curve E over F-q[x], asymptotically in the limit as the degree of the twists tends to infinity. We also compute moments involving ...