caa a22 4500 388046953 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199804 xx s 000 0 eng 10.1017/S1446788700001683 doi S1446788700001683 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700001683 Masser David Mathematisches Institut Universität Basel Rheinsprung 21 4051 Basel Switzerland Multiplicative isogeny estimates [Elektronische Daten] [David Masser] The theory of isogeny estimates for Abelian varieties provides ‘additive bounds' of the form ‘d is at most B' for the degrees d of certain isogenies. We investigate whether these can be improved to ‘multiplicative bounds' of the form ‘d divides B'. We find that in general the answer is no (Theorem 1), but that sometimes the answer is yes (Theorem 2). Further we apply the affirmative result to the study of exceptional primes in connexion with modular Galois representations coming from elliptic curves: we prove that the additive bounds for of Masser and Wüstholz (1993) can be improved to multiplicative bounds (Theorem 3). Copyright © Australian Mathematical Society 1998 11G10(14K02) nationallicence 11G05 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 64/2(1998-04), 178-194 1446-7887 64:2<178 1998 64 JAZ https://doi.org/10.1017/S1446788700001683 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700001683 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Masser David Mathematisches Institut Universität Basel Rheinsprung 21 4051 Basel Switzerland NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 64/2(1998-04), 178-194 1446-7887 64:2<178 1998 64 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge