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...
More precisely, for certain algebro-geometric families of elliptic curves defined over the function field of a fixed curve over a finite field, we give strong quantitative bounds for the number of elements in the family for which the relevant L-functions have their zeros as linearly independent ...
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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 formula for \(...
We study the special value at 2 of L-functions of modular forms of weight 2 on congruence subgroups of the modular group. We prove an explicit version of Beilinson's theorem for the modular curve X_1(N). When N is prime, we deduce that the target space of Beilinson's regulator map ...
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 VPK, Gronvik K: Preparation and characterization of specific monoclonal antibodies for the detection of adult worm infections in ...
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
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 ...
Low-lying zeros in families of elliptic curve $L$-functions over function fieldsPatrick MeisnerAnders Sdergren
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...