TY - JOUR
T1 - A remark on Nesterenko's theorem for Ramanujan functions
AU - Elsner, Carsten
AU - Shimomura, Shun
AU - Shiokawa, Iekata
PY - 2010/1
Y1 - 2010/1
N2 - We study the algebraic independence of values of the Ramanujan q-series. It is proved that, for any distinct positive integers i, j satisfying (i, j)≠(1, 3) and for any with 0<{pipe}q{pipe}<1, the numbers A1(q), A2i+1(q), A2j+1(q) are algebraically independent over. Furthermore, the q-series A2i+1(q) and A2j+1(q) are algebraically dependent over if and only if (i, j)=(1, 3).
AB - We study the algebraic independence of values of the Ramanujan q-series. It is proved that, for any distinct positive integers i, j satisfying (i, j)≠(1, 3) and for any with 0<{pipe}q{pipe}<1, the numbers A1(q), A2i+1(q), A2j+1(q) are algebraically independent over. Furthermore, the q-series A2i+1(q) and A2j+1(q) are algebraically dependent over if and only if (i, j)=(1, 3).
KW - Algebraic independence
KW - Nesterenko's theorem
KW - Ramanujan functions
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U2 - 10.1007/s11139-009-9163-3
DO - 10.1007/s11139-009-9163-3
M3 - Article
AN - SCOPUS:75549086655
VL - 21
SP - 211
EP - 221
JO - The Ramanujan Journal
JF - The Ramanujan Journal
SN - 1382-4090
IS - 2
ER -