Title Discrete universality theorem for L-functions of elliptic curves /
Translation of Title Diskreti universalumo teorema elipsinių kreivių L-funkcijoms.
Authors Čeponienė, Jurgita ; Garbaliauskienė, Virginija ; Garbaliauskas, Antanas
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Is Part of Jaunųjų mokslininkų darbai. 2010, nr.3(28), p.131-135.. ISSN 1648-8776
Keywords [eng] Elliptic curve ; L-functio ; Universality ; Limit theorem ; Probability measure ; Weak convergence
Abstract [eng] Let E be an elliptic curve over the field of rational numbers Q defined by the Weierstrass equation y2 = x3 + ax+b, x3 + ax + b, aa,, bb ∈Z Z. Denote by Δ = –16(4a3 + 27b2) the discriminant of the curve E, and suppose that Δ ≠ 0. Then the roots of the cubic x3 + ax+b are distinct, and the curve E is non-singular. In the paper there is done a research on discrete universality theorems (in Voronin’s sense) for L-functions of the curve E defined by Euler product Π Π Δ − − − Δ         + −         = − | 1 2 1 1 | ( ) 1 ( ) 1 ( ) 1 , p s s p E s p p p p L s λ p λ where p is prime number, ν ( p) is the number of solutions of the congruence y2 = x3 + ax+b (mod p), λ (p) = p – v(p), and s = σ + it is a complex variable. We use the difference of an arithmetical progression h > 0 h > 0 such that       h exp 2πk is irrational for some k ≠ 0 . The proof of the universality for L-functions of elliptic curves is based on discrete limit theorems in the sense of weak convergence of probability measures in functional spaces.
Type Journal article
Language English
Publication date 2010