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...
Furthermore, L(u,E) satisfies the functional equationL(u,E)=ϵ(E)(qu)nEL(1qu,E), where ϵ(E)∈{±1} is the root number of the elliptic curve E. We are interested in investigating the one-level density of the zeros of these L-functions. That is, for an even Schwartz test ...
Let F F be a function field of characteristic p>0 p>0 , \F/F \F/F a Galois extension with Gal(\F/F)\simeq \Z_l^d Gal(\F/F)\simeq \Z_l^d (for some prime leq p leq p ) and E/F E/F a non-isotrivial elliptic curve. We study the behaviour of Selmer groups Sel_E(...
Introduction In =-=[24]-=- we showed that large analytic ranks are ubiquitous in towers of function fields. For example, if k is a finite field and E is an elliptic curve over K = k(t) whose j-invariant is not in k, then after...Ulmer, D.: L-functions with large analytic ...
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 ...
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 ...
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 curvePlus/minus p-adic L-functionIwasawa main conjectureIn this paper, I discuss the construction of the p-adic L-function attached to a Hilbert modular form f, supersingular or ordinary, which turns out to be the non-archimedean Mellin transform of an h-admissible measure. And h ...
Low-lying zeros in families of elliptic curve $L$-functions over function fieldsPatrick MeisnerAnders Sdergren
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...