Title The Universality of Degrees of L-Functions of Elliptic Curves
Translation of Title Elipsinių kreivių L-funkcijų laipsnių universalumas.
Another Title Elipsinių kreivių l-funkcijų laipsnių universalumas.
Authors Latakas, Martynas ; Garbaliauskienė, Virginija ; Garbaliauskas, Antanas
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Is Part of Jaunųjų mokslininkų darbai = Journal of Young Scientists. 2009, nr. 3(24), p. 178-182.. ISSN 1648-8776
Keywords [eng] Elliptic curve ; L-function ; Universality ; Limit theorem
Abstract [eng] Let E be an elliptic non-singular curve over the field of rational numbers Q defined by the Weierstrass equation y2 = x3 + ax+ b, a, b ∈ Z. Let us denote by Δ = –16(4a3 + 27b2) the discriminant of the curve E. For each prime p let us mark the number of solutions of congruence y2 = x3 + ax+ b(mod p) v(p) and let λ(p) = p – v(p). The L-function LE(s) of elliptic curves, where s = σ + it is a complex variable, is defined by Euler product where p is prime number, v(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. In the paper, a survey on universality theorems (in Voronin’s sense) for L-functions and the degrees of L-functions of elliptic curves over the field of rational numbers is given. The proof of the universality of L-functions of elliptic curves is based on limit theorems in the sense of weak convergence of probability measures in functional spaces.
Type Journal article
Language English
Publication date 2009