OFFSET
1,5
LINKS
FORMULA
a(n) is multiplicative with a(2^e) = (-1)^e, a(13^e) = 1, else a(p^e) = a(p) * a(p^(e-1)) - p * a(p^(e-2)) where a(p) = p+1 minus number of points of elliptic curve modulo p including point at infinity.
G.f. is a period 1 Fourier series which satisfies f(-1 / (26 t)) = 26 (t / i)^2 f(t) where q = exp(2 Pi i t).
EXAMPLE
G.f. = q - q^2 + q^3 + q^4 - 3*q^5 - q^6 - q^7 - q^8 - 2*q^9 + 3*q^10 + ...
PROG
(PARI) {a(n) = if( n<1, 0, ellak( ellinit([ 1, 0, 1, 0, 0], 1), n))};
(PARI) {a(n) = if( n<1, 0, ellak( ellinit([ 1, 0, -1, 1, 0], 1), n))};
(Magma) A := Basis( CuspForms( Gamma0(26), 2), 76); A[1] - A[2];
(Sage)
def a(n):
return EllipticCurve("26a3").an(n) # Robin Visser, Sep 30 2023
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Michael Somos, Nov 24 2014
STATUS
approved