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...
M.: Symmetric powers of elliptic curve L-functions - Martin, Watkins () Citation Context ...rect. 6.5. Symmetric power L-functions. Similar to questions about the vanishing of L(E, s), we can ask about the vanishing of the symmetric power L-functions L(Sym 2k−1 E, s). We refer...
Let be the L-function of an elliptic curve E defined over the rational field . Assuming the Birch–Swinnerton-Dyer conjectures, we examine special values of the rth derivatives, L (r)(E, 1, χ), of twists by Dirichlet characters of when L(E, 1, χ)==L (r1)(E, 1, χ)=0....
Let E be an elliptic curve defined over Fq(T) given by the minimal Weierstrass equation y2=x3+Ax+B, where A,B∈Fq[T], and such that the prime at infinity has additive reduction.1 Then the L-function attached to E is (cf., e.g., [34, Lecture 1])(1.1)L(u,E):=∏P|ΔE(...
Chapter1ModularformsandtheShimura-TaniyamaConjecture 1.1Ellipticfunctions1.2Modularforms1.3Examples 1.4Heckeoperatorsandeigenforms1.5L-functions1.6Modularformsofhigherlevel Chapter1ModularformsandtheShimura-TaniyamaConjecture 1.7Ellipticcurves 1.8Conjectures,andthetheoremofWiles,etal ...
distribution of zerosWe study a subtle inequity in the distribution of unnormalized differences between imaginary parts of zeros of the Riemann zeta function, which was observed by a number of authors. We establish a precise measure which explains the phenomenon, that the location of each Riemann ...
Dwork[5] expressed the unit root of a non-supersingular elliptic curve y 2 = x(x − 1)(x − λ) in termsof the Gaussian hypergeometric function F( 12 ,12 ,1;λ). This analysis motivated Dwork’s generalstudy of p-adic periods. For the unit root of the family of Kloosterman ...
Here we use the L-functions ratios conjectures to calculate the 1-level density for the family of even quadratic twists of an elliptic curve L-function... DK Huynh,JP Keating,NC Snaith - 《Journal of Number Theory》 被引量: 39发表: 2008年 Journal: PROCEEDINGS OF THE LONDON MATHEMATICAL SO...
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(...
Using the idea of Sinnott, Gillard and Schneps, we prove the μ-invariant is zero for the two-variable primitive p-adic L-function constructed by Kang (2012), which arises naturally in the study of Iwasawa theory for an elliptic curve with complex multiplication (CM).YunLing Kang...