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Nagao has recently given a conjectural limit formula for the rank of an elliptic surface E in terms of a weighted average of bral Frobenius trace values. We show that Tate's conjecture on the order of vanishing of L 2 (E; s) essentially implies Nagao's formula; in particular, we prove Nagao's formula for rational elliptic surfaces. In the case that E is a… (More)

Let E/Q be an elliptic curve with a fixed modular parametrization ΦE : X0(N) → E and let P1, . . . , Pr ∈ E(Q̄) be Heegner points attached to the rings of integers of distinct quadratic imaginary field k1, . . . , kr. We prove that if the odd parts of the class numbers of k1, . . . , kr are larger than a constant C = C(E,ΦE) depending only on E and ΦE ,… (More)

Some results are obtained on the group of rational points on elliptic curves over infinite algebraic number fields. A certain naturally defined class of Dedekind domains, elliptic Dedekind domains, are described and it is shown that every countable abelian group can be realized as the class group of an elliptic Dedekind domain. Introduction. Let E be an… (More)

- Michael Rosen
- 2008

Let X = {X(t), t ∈ R+} be a real valued symmetric Lévy process with continuous local times {Lt , (t, x) ∈ R+ × R} and characteristic function EeiλX(t) = e−tψ(λ). Let σ 0(x− y) = 4 π ∞ ∫ 0 sin λ(x−y) 2 ψ(λ) dλ. If σ2 0(h) is concave, and satisfies some addtional very weak regularity conditions, then for any p ≥ 1, and all t ∈ R+

- Michael Daub, Jaclyn Lang, Mona Merling, Allison M. Pacelli, Natee Pitiwan, Michael Rosen
- 2010

It is known that infinitely many number fields and function fields of any degree m have class number divisible by a given integer n. However, significantly less is known about the indivisibility of class numbers of such fields. While it’s known that there exist infinitely many quadratic number fields with class number indivisible by a given prime, the… (More)

- Michael Rosen
- 2012

A friend of mine in the UK Paddy Walsh has passed on to me your recent ruminations on “How genre theory saved the world”. I note that Paddy is a former subject English teacher and SNS English consultant, and familiar with work done using genre theory in the UK. As I was one of the genre theorists with whom you exchanged articles in English in Australia a… (More)

- Michael Rosen
- 2011

ness of private life: Hegel develops private rights and morals as such abstractions, from which it does not follow, for him, that the state or ethical life [Sittlichkeit] of which they are presuppositions can be nothing but the society (the social life) of these illusions; 9 "Hegel calls private rights the rights of abstract personality, or abstract rights.… (More)

- John L. Markley, Hideo Akutsu, +88 authors Shigeyuki Yokoyama
- Nature Structural &Molecular Biology
- 2012

volume 19 number 9 SePTember 2012 nature structural & molecular biology of intrinsically disordered proteins, development of automated analysis of NMR data, solid-state NMR and NMR-based metabolomics. With the budget cuts that the BMRB has suffered (reduced by 40%, compared to the previous operating budget), we currently are at the minimal level of keeping… (More)

- Michael Rosen, Michael D A Vickers
- European journal of anaesthesiology
- 2014

- Vivien A. Schmidt, Andrew Martin, +15 authors Kathrin Zippel
- 2011

1 ces papers open forum # 3 Comparative political economists who use historical institutionalism have made great contributions in describing what happened in cases of political economic change in advanced industrialized democracies, but they have great difficulty explaining much of why this happened. This paper argues that a discursive institutionalist… (More)