Arithmetic properties of coefficients of L-functions of elliptic curves
Küçük Resim Yok
Tarih
2018
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
SPRINGER WIEN
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Let n = 1 ann -s be the L-series of an elliptic curve E defined over the rationals without complex multiplication. In this paper, we present certain similarities between the arithmetic properties of the coefficients {an}8 n= 1 and Euler's totient function.(n). Furthermore, we prove that both the set of n such that the regular polygon with | an| sides is ruler-and-compass constructible, and the set of n such that n-an + 1 =.(n) have asymptotic density zero. Finally, we improve a bound of Luca and Shparlinski on the counting function of elliptic pseudoprimes.
Açıklama
Anahtar Kelimeler
Rational elliptic curves, Chebotarev Density Theorem, Arithmetic functions, L-functions, Euler's totient function, Elliptic pseudoprimes
Kaynak
MONATSHEFTE FUR MATHEMATIK
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
Cilt
187
Sayı
2