TY - JOUR

T1 - A remark on Nesterenko's theorem for Ramanujan functions

AU - Elsner, Carsten

AU - Shimomura, Shun

AU - Shiokawa, Iekata

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

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 -