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...
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....
26 Zeros of linear combinations of Dirichlet L-functions on the critical line 48:49 The rank of elliptic curves 40:40 A Weyl-type inequality for irreducible elements in function fields, with applica 49:34 BALOG ANTAL_ ON THE L1 NORM OF TRIGONOMETRIC POLYNOMIALS WITH MULTIPLICATIVE COE 2:03:...
Finally, we improve a bound of Luca and Shparlinski on the counting function of elliptic pseudoprimes. 展开 关键词: Rational elliptic curves Chebotarev Density Theorem Arithmetic functions L-functions Euler’s totient function Elliptic pseudoprimes 年份: 2018 ...
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...
L-functionsRandom matrix theoryWe present some numerical results on the distribution of nonzero central values of elliptic curve L-functions. We compare the family of elliptic curves Ea,b:y2=x3+ax+b with (a,b) ranging over a large box, and Cremona's list of all elliptic curves with ...
title='L-functions of GL(%s) Maass Forms'% degree, **info) 开发者ID:davidpeterroberts,项目名称:lmfdb,代码行数:7,代码来源:main.py 示例6: l_function_dirichlet_browse_page ▲点赞 1▼ defl_function_dirichlet_browse_page():info = {"bread": get_bread(1, [])} ...
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 ...
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...
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 ...