caa a22 4500 386386188 CHVBK 20180307112059.0 cr unu---uuuuu 161130e198911 xx s 000 0 eng 10.1017/S0305004100068122 doi S0305004100068122 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100068122 Flach Matthias Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, CB2 1SB Periods and special values of the hypergeometric series [Elektronische Daten] [Matthias Flach] The aim of this paper is to complement results by Wolfart [14] about algebraic values of the classical hypergeometric series for rational parameters a, b, c and algebraic arguments z. Wolfart essentially determines the set of a, b, c ,z for which F(a, b, c; z) and indicates, in a joint paper with F. Beukers[1], that some of these values can be expressed in terms of special values of modular forms. This method yields a few strikingly explicit identities like but it does not give general statements about the nature of the algebraic values in question. In this paper we identify F(a, b, c; z) as a generator of a Kummer extension of a certain number field depending on z, which in particular bounds its degree as an algebraic number in terms of the degree of z. Our theorem in §2 seems to be the most precise statement one can make in general but sometimes improvements are possible as we point out at the end of §2. Copyright © Cambridge Philosophical Society 1989 Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/3(1989-11), 389-401 0305-0041 106:3<389 1989 106 PSP https://doi.org/10.1017/S0305004100068122 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100068122 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Flach Matthias Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, CB2 1SB NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 106/3(1989-11), 389-401 0305-0041 106:3<389 1989 106 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge