Results 31 to 40 of about 142 (128)
Arithmetic of cyclotomic fields and Fermat-type equations [PDF]
, 1994 Let l be any odd prime, and ζ a primitive l-th root of unity. Let C_l be the l-Sylow subgroup of the ideal class group of Q(ζ). The Teichmüller character w : Z_l → Z^*_l is given by w(x) = x (mod l), where w(x) is a p-1-st root of unity, and x ∈ Z_l ...
Sitaraman, Sankar
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Investigation of the gravitational lens effect with differential topology
, 2022 In this thesis, the methods of differential topology are used to study the gravitational lensing effect. First, the reader is taken on a brief tour through the basics of black holes, wormholes, gravitational lensing and the mathematical tools of Fermat's
Halla, Mourad
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f$f$‐Diophantine sets over finite fields via quasi‐random hypergraphs from multivariate polynomials
Mathematika, Volume 72, Issue 2, April 2026.Abstract We investigate f$f$‐Diophantine sets over finite fields via new explicit constructions of families of quasi‐random hypergraphs from multivariate polynomials. In particular, our construction not only offers a systematic method for constructing quasi‐random hypergraphs but also provides a unified framework for studying various hypergraphs ...
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
wiley +1 more source
Variable selection via thresholding
Scandinavian Journal of Statistics, Volume 53, Issue 1, Page 207-237, March 2026.Abstract Variable selection comprises an important step in many modern statistical inference procedures. In the regression setting, when estimators cannot shrink irrelevant signals to zero, covariates without relationships to the response often manifest small but nonzero regression coefficients.
Ka Long Keith Ho, Hien Duy Nguyen
wiley +1 more source
Sophie Germain's theorem for prime pairs p, 6p + 1
, 1987 In 1823, Sophie Germain (Mem. Acad. Sci. Inst. France 6 (1823), 1–60) showed that if p, 2p + 1 are both odd primes then the so-called “First Case” of Fermat's Last Theorem holds for p.
Granville, Andrew
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Arithmetic progressions at the Journal of the LMS
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the papers P. Erdős and P. Turán, On some sequences of integers, J. London Math. Soc. (1) 11 (1936), 261–264 and K. F. Roth, On certain sets of integers, J. London Math. Soc. (1) 28 (1953), 104–109, both foundational papers in the study of arithmetic progressions in sets of integers, and their subsequent influence.
Ben Green
wiley +1 more source
Diophantine tuples and product sets in shifted powers
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley +1 more source
Explicit Estimates in Inter-universal Teichmüller Theory [PDF]
, 2020 In the final paper of a series of papers concerning inter- universal Teichmüller theory, Mochizuki verified various numerically non-effective versions of the Vojta, ABC, and Szpiro Conjectures over number fields.
MOCHIZUKI, Shinichi +4 more
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On the Electromagnetic Energy Flow Along Geodesics
Radio Science, Volume 61, Issue 1, January 2026.Abstract We present a field‐theoretic framework for modeling electromagnetic energy propagation in heterogeneous media by introducing the concept of electromagnetic geodesics. Unlike traditional ray optics, which assumes either a straight‐line propagation or a simple bending in refractive media, our approach formulates wave propagation as geodetic ...
Jacob T. Fokkema, Peter M. van den Berg
wiley +1 more source
Sophie Germain And The Struggles Of Women Mathematicians During The French Revolution [PDF]
, 2018 In this thesis, I analyze the social conditions of women during a time that they were not encouraged to become educated. Throughout the period of the French Revolution and the Enlightenment, women struggled to penetrate into scientific fields as they ...
NC DOCKS at Appalachian State University +1 more
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