Results 41 to 50 of about 217 (158)
On the Exponents of Ideal Class Groups of Cyclotomic Fields [PDF]
Proceedings of the American Mathematical Society, 1993 It will be proved that the ideal class group of the cyclotomic field of 65th roots of unity is of type ( 4 , 4
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Syntomic cohomology and real topological cyclic homology
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract We define motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions of syntomic cohomology.
Doosung Park
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Quantum recurrences and the arithmetic of Floquet dynamics [PDF]
QuantumThe Poincaré recurrence theorem shows that conservative systems in a bounded region of phase space eventually return arbitrarily close to their initial state after a finite amount of time.
Amit Anand +3 more
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Ideal class groups of cyclotomic number fields I [PDF]
Acta Arithmetica, 1995 Using an idea going back to Scholz, we construct unramified abelian extensions of cyclotomic extensions of number fields.
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On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
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Structured Module Lattice-based Cryptography
Transactions on Cryptographic Hardware and Embedded SystemsThe ongoing transition to Post-Quantum Cryptography (PQC) has highlighted the need for cryptographic schemes that offer high security, strong performance, and fine-grained parameter selection.
Joppe W. Bos +3 more
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On the coefficients of a class of ternary cyclotomic polynomials
Glasnik matematički, 2023 A cyclotomic polynomial \(\Phi_n(x)\) is said to be flat if its nonzero coefficients involve only \(\pm1\). In this paper, for odd primes \(p \lt q \lt r\) with \(q\equiv 1\pmod p\) and \(9r\equiv \pm1\pmod {pq}\), we prove that \(\Phi_{pqr}(x)\) is flat if and only if \(p=5\), \(q\geq 41\), and \(q\equiv 1\pmod 5\).
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The asymptotic Mahler measure of Gaussian periods
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract We construct a sequence of cyclotomic integers (Gaussian periods) of particularly small Mahler measure/height. We study the asymptotics of their Mahler measure as a function of their conductor, to find that the growth rate is the (multivariate) Mahler measure of a family of log Calabi–Yau varieties of increasing dimension.
Gunther Cornelissen +2 more
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ON THE DIVISORS OF THE SECOND FACTOR OF THE CLASS NUMBER OF A CYCLOTOMIC FIELD [PDF]
Proceedings of the National Academy of Sciences, 1955 In Hinblick auf die Fermatsche Vermutung wendet Verf. auf ein Kriterium [\textit{D. H. Lehmer}, \textit{E. Lehmer} und Verf., Proc. Natl. Acad. Sci. USA 40, 25--33 (1954; Zbl 0055.04004)], das unter der Voraussetzung \(h_2\equiv 0 \pmod l\) \((h_2\) zweiter Klassenzahlfaktor des Körpers der \(l\)-ten Einheitswurzeln, \(l\) ungerade Primzahl) gilt, eine
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Cpn$C_{p^n}$‐equivariant Mahowald invariants
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract The classical Mahowald invariant is an operation that systematically produces new elements in the stable homotopy groups of spheres from known ones. We introduce the Cpn$C_{p^n}$‐Mahowald invariant: a relation π★SCpn−1⇀π*S$\pi _\star S_{\mathchoice{{ C_{p^{n-1}}}}{{\textstyle C_{p^{n-1}}}}{{\scriptstyle C_{p^{n-1}}}}{{\scriptscriptstyle C_{p ...
William Balderrama +2 more
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