TY - JOUR
T1 - On the value set of the Ramanujan function
AU - Shparlinski, Igor E.
PY - 2005/12
Y1 - 2005/12
N2 - We give lower bounds on the number of distinct values of the Ramanujan function τ(n),n≦x, and on the number of distinct residues of τ(n),n≦x, modulo a prime ℓ. We also show that for any prime ℓ the values τ(n),n≦ℓ4, form a finite additive basis modulo ℓ.
AB - We give lower bounds on the number of distinct values of the Ramanujan function τ(n),n≦x, and on the number of distinct residues of τ(n),n≦x, modulo a prime ℓ. We also show that for any prime ℓ the values τ(n),n≦ℓ4, form a finite additive basis modulo ℓ.
UR - http://www.scopus.com/inward/record.url?scp=29844456805&partnerID=8YFLogxK
U2 - 10.1007/s00013-005-1322-1
DO - 10.1007/s00013-005-1322-1
M3 - Article
AN - SCOPUS:29844456805
VL - 85
SP - 508
EP - 513
JO - Archiv der Mathematik
JF - Archiv der Mathematik
SN - 0003-889X
IS - 6
ER -