William Stein

William Stein
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William Stein

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Solar and Stellar Astrophysics (22)
Mathematics - Number Theory (9)
High Energy Astrophysical Phenomena (3)
Mathematics - Algebraic Geometry (2)
Computer Science - Computers and Society (1)
Mathematics - History and Overview (1)
Mathematics - Numerical Analysis (1)

Publications Authored By William Stein

In 2016 May, the intermediate polar FO~Aqr was detected in a low state for the first time in its observational history. We report time-resolved photometry of the system during its initial recovery from this faint state. Our data, which includes high-speed photometry with cadences of just 2 sec, shows the existence of very strong periodicities at 22. Read More

How black holes accrete surrounding matter is a fundamental, yet unsolved question in astrophysics. It is generally believed that matter is absorbed into black holes via accretion disks, the state of which depends primarily on the mass-accretion rate. When this rate approaches the critical rate (the Eddington limit), thermal instability is supposed to occur in the inner disc, causing repetitive patterns of large-amplitude X-ray variability (oscillations) on timescales of minutes to hours. Read More

Continuing the project described by Kato et al. (2009, arXiv:0905.1757), we collected times of superhump maxima for 128 SU UMa-type dwarf novae observed mainly during the 2015-2016 season and characterized these objects. Read More

We describe the role the open-source software community plays in fixing bugs through a case study of a problem with integer determinant computations in SageMath. Read More

We present optical photometry of a WZ Sge-type dwarf nova (DN), ASASSN-15jd. Its light curve showed a small dip in the middle of the superoutburst in 2015 for the first time among WZ Sge-type DNe. The unusual light curve implies a delay in the growth of the 3:1 resonance tidal instability. Read More

We observed the first-ever recorded outburst of PM J03338+3320, the cataclysmic variable selected by proper-motion survey. The outburst was composed of a precursor and the main superoutburst. The precursor outburst occurred at least 5 d before the maximum of the main superoutburst. Read More

Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava-Shankar studying the average sizes of $n$-Selmer groups, have given new upper bounds on the average algebraic rank in families of elliptic curves over $\mathbb{Q}$ ordered by height. We describe databases of elliptic curves over $\mathbb{Q}$ ordered by height in which we compute ranks and $2$-Selmer group sizes, the distributions of which may also be compared to these theoretical results. Read More

Authors: Taichi Kato, Franz-Josef Hambsch, Pavol A. Dubovsky, Igor Kudzej, Berto Monard, Ian Miller, Hiroshi Itoh, Seiichiro Kiyota, Kazunari Masumoto, Daiki Fukushima, Hiroki Kinoshita, Kazuki Maeda, Jyunya Mikami, Risa Matsuda, Naoto Kojiguchi, Miho Kawabata, Megumi Takenaka, Katsura Matsumoto, Enrique de Miguel, Yutaka Maeda, Tomohito Ohshima, Keisuke Isogai, Roger D. Pickard, Arne Henden, Stella Kafka, Hidehiko Akazawa, Noritoshi Otani, Sakiko Ishibashi, Minako Ogi, Kenji Tanabe, Kazuyoshi Imamura, William Stein, Kiyoshi Kasai, Tonny Vanmunster, Peter Starr, Elena P. Pavlenko, Oksana I. Antonyuk, Kirill A. Antonyuk, Aleksei A. Sosnovskij, Nikolaj V. Pit, Julia V. Babina, Aleksandr Sklyanov, Rudolf Novak, Arto Oksanen, Shawn Dvorak, Raul Michel, Gianluca Masi, Colin Littlefield, Joseph Ulowetz, Sergey Yu. Shugarov, Polina Yu. Golysheva, Drahomir Chochol, Viktoriia Krushevska, Javier Ruiz, Tamas Tordai, Etienne Morelle, Richard Sabo, Hiroyuki Maehara, Michael Richmond, Natalia Katysheva, Kenji Hirosawa, William N. Goff, Franky Dubois, Ludwig Logie, Steve Rau, Irina B. Voloshina, Maksim V. Andreev, Kazuhiko Shiokawa, Vitaly V. Neustroev, George Sjoberg, Sergey Zharikov, Nick James, Greg Bolt, Tim Crawford, Denis Buczynski, Lewis M. Cook, Christopher S. Kochanek, Benjamin Shappee, Krzysztof Z. Stanek, Jose L. Prieto, Denis Denisenko, Hideo Nishimura, Masaru Mukai, Shizuo Kaneko, Seiji Ueda, Rod Stubbings, Masayuki Moriyama, Patrick Schmeer, Eddy Muyllaert, Jeremy Shears, Robert J. Modic, Kevin B. Paxson

Continuing the project described by Kato et al. (2009, arXiv:0905.1757), we collected times of superhump maxima for 102 SU UMa-type dwarf novae observed mainly during the 2014-2015 season and characterized these objects. Read More

We present the 13-year light curve of HW Boo between 2001 May and 2014 May. We identified 12 outbursts, which typically lasted 2 to 5 days, with an amplitude of 2.7 to 3. Read More

Affiliations: 1Kyoto U

Continuing the project described by Kato et al. (2009, PASJ, 61, S395, arXiv:0905.1757), we collected times of superhump maxima for 56 SU UMa-type dwarf novae mainly observed during the 2013-2014 season and characterized these objects. Read More

We carried out the photometric observations of the SU UMa-type dwarf nova ER UMa during 2011 and 2012, which showed the existence of persistent negative superhumps even during the superoutburst. We performed two-dimensional period analysis of its light curves by using a method called "least absolute shrinkage and selection operator" (Lasso) and "phase dispersion minimization" (PDM) analysis, and we found that the period of negative superhumps systematically changed between a superoutburst and the next superoutburst. The trend of the period change can beinterpreted as reflecting the change of the disk radius. Read More


Continuing the project described by Kato et al. (2009a, arXiv:0905.1757), we collected times of superhump maxima for SU UMa-type dwarf novae mainly observed during the 2012-2013 season. Read More

Mazur, Tate, and Teitelbaum gave a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for elliptic curves. We provide a generalization of their conjecture in the good ordinary case to higher dimensional modular abelian varieties over the rationals by constructing the p-adic L-function of a modular abelian variety and showing that it satisfies the appropriate interpolation property. This relies on a careful normalization of the p-adic L-function, which we achieve by a comparison of periods. Read More


Continuing the project described by Kato et al. (2009, arXiv:0905.1757), we studied 86 SU UMa-type dwarf novae. Read More

We report on a discovery of "negative" superhumps during the 2011 January superoutburst of ER UMa. During the superoutburst which started on 2011 January 16, we detected negative superhumps having a period of 0.062242(9) d, shorter than the orbital period by 2. Read More

In 2011 October an optical transient was reported in Pegasus as a possible nova. The object had an ultraviolet counterpart, GALEX J215818.5+241924. Read More

The aim of the present paper is to give evidence, largely numerical, in support of the non-commutative main conjecture of Iwasawa theory for the motive of a primitive modular form of weight k>2 over the Galois extension of Q obtained by adjoining to Q all p-power roots of unity, and all p-power roots of a fixed integer m>1. The predictions of the main conjecture are rather intricate in this case because there is more than one critical point, and also there is no canonical choice of periods. Nevertheless, our numerical data agrees perfectly with all aspects of the main conjecture, including Kato's mysterious congruence between the cyclotomic Manin p-adic L-function, and the cyclotomic p-adic L-function of a twist of the motive by a certain non-abelian Artin character of the Galois group of this extension. Read More

We describe a tabulation of (conjecturally) modular elliptic curves over the field Q(sqrt(5)) up to the first curve of rank 2. Using an efficient implementation of an algorithm of Lassina Dembele, we computed tables of Hilbert modular forms of weight (2,2) over Q(sqrt(5)), and via a variety of methods we constructed corresponding elliptic curves, including (again, conjecturally) all elliptic curves over Q(sqrt(5)) that have conductor with norm less than or equal to 1831. Read More

We report unfiltered photometry of SDSS J112003.40+663632.4 during the 2011 February outburst which revealed the presence of superhumps with peak-to-peak amplitude of up to 0. Read More

We report CCD photometry of the superoutburst of the dwarf nova V1212 Tau obtained during 2011 January and February. The outburst amplitude was at least 6 magnitudes and it lasted at least 12 days. Three distinct superhump regimes were observed. Read More

Continuing the project described by Kato et al. (2009, PASJ 61, S395, arXiv:0905.1757), we collected times of superhump maxima for 51 SU UMa-type dwarf novae mainly observed during the 2010-2011 season. Read More

We report unfiltered photometry during the first confirmed superoutburst of the recently discovered dwarf nova, SDSS J073208.11+413008.7 and conclude that it is a member of the SU UMa family. Read More

Let f be a non-CM newform of weight k > 1. Let L be a subfield of the coefficient field of f. We completely settle the question of the density of the set of primes p such that the p-th coefficient of f generates the field L. Read More

Kolyvagin used Heegner points to associate a system of cohomology classes to an elliptic curve over $\Q$ and conjectured that the system contains a non-trivial class. His conjecture has profound implications on the structure of Selmer groups. We provide new computational and theoretical evidence for Kolyvagin's conjecture. Read More

We study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. We make a precise conjecture about the indexes of Hecke algebras in their normalisation which implies (if true) the conjecture that there are no mod p congruences between non-conjugate newforms of weight 2 and level Gamma_0(p). Read More

Suppose $p$ is a prime of the form $u^2+64$ for some integer $u$, which we take to be 3 mod 4. Then there are two Neumann--Setzer elliptic curves $E_0$ and $E_1$ of prime conductor $p$, and both have Mordell--Weil group $\Z/2\Z$. There is a surjective map $X_0(p)\xrightarrow{\pi} E_0$ that does not factor through any other elliptic curve (i. Read More