An elliptic curve test of the L-Functions Ratios Conjecture
نویسندگان
چکیده
منابع مشابه
An Orthogonal Test of the L-functions Ratios Conjecture, Ii
Recently Conrey, Farmer, and Zirnbauer [CFZ1, CFZ2] developed the Lfunctions Ratios conjecture, which gives a recipe that predicts a wealth of statistics, from moments to spacings between adjacent zeros and values of L-functions. The problem with this method is that several of its steps involve ignoring error terms of size comparable to the main term; amazingly, the errors seem to cancel and th...
متن کاملAn Orthogonal Test of the L-functions Ratios Conjecture
We test the predictions of the L-functions Ratios Conjecture for the family of cuspidal newforms of weight k and level N , with either k fixed and N → ∞ through the primes or N = 1 and k → ∞. We study the main and lower order terms in the 1-level density. We provide evidence for the Ratios Conjecture by computing and confirming its predictions up to a power savings in the family’s cardinality, ...
متن کاملA Symplectic Test of the L-Functions Ratios Conjecture
Recently Conrey, Farmer and Zirnbauer [CFZ1, CFZ2] conjectured formulas for the averages over a family of ratios of products of shifted L-functions. Their L-functions Ratios Conjecture predicts both the main and lower order terms for many problems, ranging from n-level correlations and densities to mollifiers and moments to vanishing at the central point. There are now many results showing agre...
متن کاملSymmetric Powers of Elliptic Curve L-Functions
The conjectures of Deligne, Bĕılinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebrogeometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloc...
متن کاملAn elliptic curve test for Mersenne primes
Let l ≥ 3 be a prime, and let p = 2 − 1 be the corresponding Mersenne number. The Lucas-Lehmer test for the primality of p goes as follows. Define the sequence of integers xk by the recursion x0 = 4, xk = x 2 k−1 − 2. Then p is a prime if and only if each xk is relatively prime to p, for 0 ≤ k ≤ l − 3, and gcd(xl−2, p) > 1. We show, in the first section, that this test is based on the successiv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2011
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2010.12.004