Limit theorems for twists of L-functions of elliptic curves

A Joint Elliott Type Theorem for Twists of L-Functions of Elliptic Curves

“…Then it was observed in [12] that the function L E (s, χ), as L E (s), is also entire one. Limit theorems for L E (s, χ) with increasing q were began to study in [6], [7], [8], [9], however, only in the half-plane of absolute convergence σ > 3 2 . In [12], a limit theorem in the space of analytic functions H(D), D = {s ∈ C : σ > 1}, for the function L E (s, χ) has been obtained.…”

A Limit Theorem for Twists of L-Functions of Elliptic Curves

“…Therefore, we briefly remind the limit theorems for the modulus and argument for twists of L-functions of elliptic curves obtained in [5] and [4], respectively.…”

Limit Theorems for Twists of L-Functions of Elliptic Curves. Ii

“…In [3], we began to study limit theorems for twisted with Dirichlet character L-functions of elliptic curves with an increasing modulus of the character, and obtained a limit theorem of such a type for the modulus of these twists. Let E be an elliptic curve over the field of rational numbers given by the Weierstrass equation y 2 = x 3 + ax + b, a, b ∈ Z, with non-zero discriminant ∆ = −16(4a 3 + 27b 2 ).…”

“…The twist L E (s, χ) with Dirichlet character χ for the function L E (s) is defined similarly. For σ > 3 2 , we have that…”