An Elliott-Type Theorem for Twists of $L$-Functions of Elliptic Curves
Matematičeskie zametki, Tome 99 (2016) no. 1, pp. 78-88.

Voir la notice de l'article provenant de la source Math-Net.Ru

A limit theorem involving an increasing modulus of the character is obtained for convolutions with the Dirichlet character of $L$-functions of elliptic curves.
Keywords: elliptic curve, $L$-function, Dirichlet character, Dirichlet series, Haar probability measure, Abelian group.
Mots-clés : Weil–Shimura–Taniyama conjecture
@article{MZM_2016_99_1_a6,
     author = {A. Laurin\v{c}ikas},
     title = {An {Elliott-Type} {Theorem} for {Twists} of $L${-Functions} of {Elliptic} {Curves}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {78--88},
     publisher = {mathdoc},
     volume = {99},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_1_a6/}
}
TY  - JOUR
AU  - A. Laurinčikas
TI  - An Elliott-Type Theorem for Twists of $L$-Functions of Elliptic Curves
JO  - Matematičeskie zametki
PY  - 2016
SP  - 78
EP  - 88
VL  - 99
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_99_1_a6/
LA  - ru
ID  - MZM_2016_99_1_a6
ER  - 
%0 Journal Article
%A A. Laurinčikas
%T An Elliott-Type Theorem for Twists of $L$-Functions of Elliptic Curves
%J Matematičeskie zametki
%D 2016
%P 78-88
%V 99
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_99_1_a6/
%G ru
%F MZM_2016_99_1_a6
A. Laurinčikas. An Elliott-Type Theorem for Twists of $L$-Functions of Elliptic Curves. Matematičeskie zametki, Tome 99 (2016) no. 1, pp. 78-88. http://geodesic.mathdoc.fr/item/MZM_2016_99_1_a6/

[1] S. Chowla, P. Erdős, “A theorem on the values of $L$-function”, J. Indian Math. Soc. (N.S.), 15 (1951), 11–18 | MR | Zbl

[2] P. D. T. A. Elliott, “On the distribution of the values of $L$-series in the half-plane $\sigma>{1}/{2}$”, Indag. Math., 33 (1971), 222–234 | DOI | MR | Zbl

[3] P. D. T. A. Elliott, “On the distribution of $\arg L(s,\chi)$ in the half-plane $\sigma>\frac{1}{2}$”, Acta Arith., 20 (1972), 155–159 | MR | Zbl

[4] E. Stankus, “Raspredelenie $L$-funktsii Dirikhle”, Litovsk. matem. sb., 15:2 (1975), 127–134 | MR | Zbl

[5] A. Laurinčikas, Limit Theorems for the Riemann Zeta-Function, Math. Appl., 352, Kluwer Acad. Publ., Dordrecht, 1996 | MR

[6] V. Garbaliauskienė, A. Laurinčikas, E. Stankus, “Limit theorems for twists of $L$-functions of elliptic curves”, Lith. Math. J., 50:2 (2010), 187–197 | DOI | MR | Zbl

[7] V. Garbaliauskienė, A. Laurinčikas, “Limit theorems for twists of $L$-functions of elliptic curves. II”, Math. Model. Anal., 17:1 (2012), 90–99 | DOI | MR | Zbl

[8] V. Garbaliauskienė, A. Laurinčikas, “Limit theorems for twists of $L$-functions of elliptic curves. IV”, Math. Model. Anal., 19:1 (2014), 66–74 | DOI | MR

[9] V. Garbaliauskienė, A. Laurinčikas, “A limit theorem for twists of $L$-functions of elliptic curves”, Math. Model. Anal., 19:5 (2014), 696–705 | DOI | MR

[10] C. Breuil, B. Conrad, F. Diamond, R. Taylor, “On the modularity of elliptic curves over $\mathbb{Q}$: wild 3-adic exercises”, J. Amer. Math. Soc., 14:4 (2001), 843–939 | DOI | MR | Zbl

[11] H. Iwaniec, E. Kowalski, Analytic Number Theory, Amer. Math. Soc. Colloq. Publ., 53, Amer. Math. Soc., Providence, RI, 2004 | MR | Zbl

[12] B. Bagchi, The Statistical Behaviuor and Universality Properties of the Riemann Zeta-Function and Other Allied Dirichlet Series, Ph.D. Thesis, Indian Stat. Institute, Calcutta, 1981

[13] P. Deligne, “Le conjecture de Weil. I”, Inst. Hâutes Études Sci. Publ. Math., 43 (1974), 273–307 | DOI | MR | Zbl

[14] M. Jutila, “On the approximate functional equation for $\zeta^2(s)$ and other Dirichlet series”, Quart. J. Math. Oxford Ser. (2), 37 (1986), 193–209 | DOI | MR | Zbl

[15] L. Kuipers, H. Niederreiter, Uniform Distribution of Sequences, Pure Appl. Math., John Wiley Sons, New York, 1974 | MR | Zbl