On embedding numbers into quaternion orders.
J. Brzezinski (1991)
Commentarii mathematici Helvetici
Yuval Z. Flicker (1988)
Compositio Mathematica
Lomadze, G. (2004)
Georgian Mathematical Journal
Dieter Klusch (1991)
Acta Arithmetica
Joachim Schwermer (1995)
Forum mathematicum
Michio Ozeki (1986)
Mathematische Zeitschrift
Hisashi Kojima (1997)
Acta Arithmetica
Ginzburg, David, Rallis, Stephen, Soudry, David (1999)
Annals of Mathematics. Second Series
T. Meurman (1988)
Journal für die reine und angewandte Mathematik
Tom Fisher (2015)
Acta Arithmetica
We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.
Jay Jorgenson (1999)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Winfried Kohnen (2004)
Acta Arithmetica
S. Raghavan, S. Böcherer (1988)
Journal für die reine und angewandte Mathematik
Richard Taylor (1989)
Inventiones mathematicae
Frazer Jarvis (1997)
Journal für die reine und angewandte Mathematik
P. Bayer, J. C. Lario (1992)
Compositio Mathematica
E. Carletti, G. Monti Bragadin, A. Perelli (1994)
Acta Arithmetica
Karolina Krawciów (2011)
Colloquium Mathematicae
This paper focuses on the Diophantine equation , with fixed α, p, and M. We prove that, under certain conditions on M, this equation has no non-trivial integer solutions if , where is an effective constant. This generalizes Theorem 1.4 of the paper by Bennett, Vatsal and Yazdani [Compos. Math. 140 (2004), 1399-1416].
Winfried Kohnen (1992)
Mathematische Annalen
Stephan Baier, Liangyi Zhao (2013)
Acta Arithmetica
We study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form [g(n)].