Results 41 to 50 of about 651 (161)

The quartic Fermat equation in Hilbert class fields of imaginary quadratic fields

, 2015
It is shown that the quartic Fermat equation x4 + y4 = 1 has nontrivial integral solutions in the Hilbert class field Σ of any quadratic field whose discriminant satisfies -d ≡ 1 (mod 8). A corollary is that the quartic Fermat equation has no nontrivial
Rodney Lynch, Morton, Patrick, Patrick Morton, Lynch, Rodney   +3 more
core   +1 more source

Properties of meromorphic solutions to certain differential-difference equations

Electronic Journal of Differential Equations, 2013
We consider the properties of meromorphic solutions to certain type of non-linear difference equations. Also we show the existence of meromorphic solutions with finite order for differential-difference equations related to the Fermat type functional ...
Xiaoguang Qi, Lianzhong Yang
doaj  

Generalized free wreath products and their operator algebras

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima‐Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity, and K‐amenability. We study qualitative properties of the associated von Neumann algebra: factoriality, primeness,
Pierre Fima, Arthur Troupel
wiley   +1 more source

Zagier’s reduction theory for indefinite binary quadratic forms and the Fermat-Pell Equation [PDF]

, 2020
We give an in depth description of indefinite binary quadratic forms with a particular emphasis on Zagier’s reduction theory for such forms. We also connect this theory with the theory of minus continued fractions and as a further application we offer a ...
Steward, Stephen Michael, NC DOCKS at The University of North Carolina at Greensboro   +1 more
core  

On the Peculiar Properties of Extremely Low Frequency Lightning Generated Whistlers Detected at Low Earth Orbit Altitudes Close to the Magnetic Equator

Geophysical Research Letters, Volume 53, Issue 10, 28 May 2026.
Abstract Lightning strikes generate broadband electromagnetic signals. At Extremely Low Frequencies (ELF), these signals partly leak into the ionosphere and produce so‐called Lightning Generated (LG) whistlers that the Absolute Scalar Magnetometers on board the ESA Swarm satellites can detect.
M. Jenner, P. Coïsson, G. Hulot, L. Chauvet, R. Deborde   +4 more
wiley   +1 more source

Is there a computable upper bound for the height of a solution of a Diophantine equation with a unique solution in positive integers?

Open Computer Science, 2017
Let Bn = {xi · xj = xk : i, j, k ∈ {1, . . . , n}} ∪ {xi + 1 = xk : i, k ∈ {1, . . . , n}} denote the system of equations in the variables x1, . . . , xn. For a positive integer n, let _(n) denote the smallest positive integer b such that for each system
Tyszka Apoloniusz
doaj   +1 more source

Proof of Fermat Last Theorem based on successive presentations of pairs of odd numbers. Solution properties of equation x^a+y^a=z^b

, 2022
A simpler proof of Fermat Last Theorem (FLT), formulated by Fermat in 1637, is suggested. The initial equation x^n + y^n = z^n is considered not in natural, but in integer numbers.
Shestopaloff, Yuri K.
core   +1 more source

Beyond Expansion IV: Traces of Thin Semigroups

Discrete Analysis, 2018
Beyond Expansion IV: Traces of Thin Semigroups, Discrete Analysis 2018:6, 27 pp. This is the fourth in a series of papers by Bourgain and Kontorovich that study the arithmetic properties of groups and semigroups of 2-by-2 integer matrices.
Jean Bourgain, Alex Kontorovich
doaj   +1 more source

The hard X‐ray ptychography endstation at the Taiwan Photon Source

Journal of Synchrotron Radiation, Volume 33, Issue 3, Page 841-847, May 2026.
The newly commissioned hard X‐ray ptychography endstation at the Taiwan Photon Source, TPS 25A2, is introduced, detailing the instrumental specifications and demonstrating a benchmark spatial resolution of 6.9 nm in 2D, showcased through the imaging of a standard test pattern, inorganic nanoparticles and a complex biological structure.Following our ...
Yi-Wei Tsai, Gung-Chian Yin, Bo-Yi Chen, Hsin-Wei Chen, Kang-Ching Chu, Chi-Yuan Cheng, Po-Wei Lee, Jhih-Min Lin, Chun-Yu Chen, Yu-Shan Huang   +9 more
wiley   +1 more source

Counting 5‐isogenies of elliptic curves over Q$\mathbb {Q}$

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract We show that the number of 5‐isogenies of elliptic curves defined over Q$\mathbb {Q}$ with naive height bounded by H>0$H > 0$ is asymptotic to C5·H1/6(logH)2$C_5\cdot H^{1/6} (\log H)^2$ for some explicitly computable constant C5>0$C_5 > 0$. This settles the asymptotic count of rational points on the genus zero modular curves X0(m)$\mathcal {X}
Santiago Arango‐Piñeros, Changho Han, Oana Padurariu, Sun Woo Park   +3 more
wiley   +1 more source