Wyniki wyszukiwania

1

Non-vanishing of modular L-functions on a disc

100%

Akbary A.

Acta Arithmetica

|

2000

|

tom 92

|

nr 4

303-318

2

On invariants of elliptic curves on average

63%

Akbary A., Felix A.

Acta Arithmetica

|

2015

|

tom 168

|

nr 1

31-70

EN

We prove several results regarding some invariants of elliptic curves on average over the family of all elliptic curves inside a box of sides A and B. As an example, let E be an elliptic curve defined over ℚ and p be a prime of good reduction for E. Let $e_E(p)$ be the exponent of the group of rational points of the reduction modulo p of E over the finite field $𝔽_p$. Let 𝓒 be the family of elliptic curves $E_{a,b} : y^2 = x^3 + ax + b$, where |a| ≤ A and |b| ≤ B. We prove that, for any c > 1 and k∈ ℕ, $1/|𝓒| ∑_{E∈𝓒} ∑_{p≤x} e_E^k(p) = C_k li(x^{k+1}) + O((x^{k+1})/(logx)^c})$ as x → ∞, as long as $A,B > exp(c_1 (logx)^{1/2})$ and $AB > x(logx)^{4+2c}$, where $c_1$ is a suitable positive constant. Here $C_k$ is an explicit constant given in the paper which depends only on k, and $li(x) = ∫_{2}^x dt/log{t}$. We prove several similar results as corollaries to a general theorem. The method of the proof is capable of improving some of the known results with $A,B > x^ϵ$ and $AB > x(logx)^δ$ to $A,B > exp(c_1 (logx)^{1/2})$ and $AB > x(logx)^δ$.

3

Lower bounds for power moments of L-functions

63%

Akbary A., Fodden B.

Acta Arithmetica

|

2012

|

tom 151

|

nr 1

11-38

4

Average distributions and products of special values of L-series

51%

Akbary A., David C., Juricevic R.

Acta Arithmetica

|

2004

|

tom 111

|

nr 3

239-268

Ograniczanie wyników

4 Acta Arithmetica

4 Akbary A.

1 David C.

1 Felix A.

1 Fodden B.

1 Juricevic R.

1 2015

1 2012

1 2004

1 2000

Non-vanishing of modular L-functions on a disc

On invariants of elliptic curves on average

Lower bounds for power moments of L-functions

Average distributions and products of special values of L-series