Results 41 to 50 of about 114 (98)

The slice spectral sequence for a motivic analogue of the connective K(1)$K(1)$‐local sphere

Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.
Abstract We compute the 2‐adic effective slice spectral sequence (ESSS) for the motivic stable homotopy groups of L$L$, a motivic analogue of the connective K(1)$K(1)$‐local sphere over prime fields of characteristic not two. Together with the analogous computation over algebraically closed fields, this yields information about the motivic K(1)$K(1 ...
Hana Jia Kong, J. D. Quigley
wiley   +1 more source

On tame ramification and centers of F$F$‐purity

Journal of the London Mathematical Society, Volume 110, Issue 4, October 2024.
Abstract We introduce a notion of tame ramification for general finite covers. When specialized to the separable case, it extends to higher dimensions the classical notion of tame ramification for Dedekind domains and curves and sits nicely in between other notions of tame ramification in arithmetic geometry. However, when applied to the Frobenius map,
Javier Carvajal‐Rojas, Anne Fayolle
wiley   +1 more source

A discrete mean value of the Riemann zeta function

Mathematika, Volume 70, Issue 4, October 2024.
Abstract In this work, we estimate the sum ∑0<ℑ(ρ)⩽Tζ(ρ+α)X(ρ)Y(1−ρ)$$\begin{align*} \sum _{0 < \Im (\rho) \leqslant T} \zeta (\rho +\alpha)X(\rho) Y(1\!-\! \rho) \end{align*}$$over the nontrivial zeros ρ$\rho$ of the Riemann zeta function where α$\alpha$ is a complex number with α≪1/logT$\alpha \ll 1/\log T$ and X(·)$X(\cdot)$ and Y(·)$Y(\cdot)$ are ...
Kübra Benli, Ertan Elma, Nathan Ng
wiley   +1 more source

Semilinear clannish algebras

Proceedings of the London Mathematical Society, Volume 129, Issue 4, October 2024.
Abstract We define a class of associative algebras generalizing ‘clannish algebras’, as introduced by the second author, but also incorporating semilinear structure, like a skew polynomial ring. Clannish algebras generalize the well‐known ‘string algebras’ introduced by Butler and Ringel.
Raphael Bennett‐Tennenhaus, William Crawley‐Boevey   +1 more
wiley   +1 more source

A functorial approach to monomorphism categories II: Indecomposables

Proceedings of the London Mathematical Society, Volume 129, Issue 4, October 2024.
Abstract We investigate the (separated) monomorphism category mono(Q,Λ)$\operatorname{mono}(Q,\Lambda)$ of a quiver over an Artin algebra Λ$\Lambda$. We show that there exists an epivalence (called representation equivalence in the terminology of Auslander) from mono¯(Q,Λ)$\overline{\operatorname{mono}}(Q,\Lambda)$ to rep(Q,mod¯Λ)$\operatorname{rep}(Q,\
Nan Gao, Julian Külshammer, Sondre Kvamme, Chrysostomos Psaroudakis   +3 more
wiley   +1 more source

Frieze patterns over algebraic numbers

Bulletin of the London Mathematical Society, Volume 56, Issue 4, Page 1417-1432, April 2024.
Abstract Conway and Coxeter have shown that frieze patterns over positive rational integers are in bijection with triangulations of polygons. An investigation of frieze patterns over other subsets of the complex numbers has recently been initiated by Jørgensen and the first two authors.
Michael Cuntz, Thorsten Holm, Carlo Pagano   +2 more
wiley   +1 more source

An Elementary Proof of the Transformation Formula for the Dedekind Eta Function

Armenian Journal of Mathematics
In this work, we give an elementary proof of the transformation formula for the Dedekind eta function under the action of the modular group $\text{PSL}\,(2,\mathbb{Z})$. We start by giving a proof of the transformation formula $\eta(\tau)$ under the transformation $\tau\to -1/\tau$, using the Jacobi triple product identity and the Poisson summation ...
Kong, Ze-Yong, Teo, Lee Peng
openaire   +3 more sources

Octonionic Magical Supergravity, Niemeier Lattices, and Exceptional & Hilbert Modular Forms

Fortschritte der Physik, Volume 72, Issue 2, February 2024.
Abstract The quantum degeneracies of Bogomolny‐Prasad‐Sommerfield (BPS) black holes of octonionic magical supergravity in five dimensions are studied. Quantum degeneracy is defined purely number theoretically as the number of distinct states in charge space with a given set of invariant labels.
Murat Günaydin, Abhiram Kidambi
wiley   +1 more source

Adelic Rogers integral formula

Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.
Abstract We formulate and prove the extension of the Rogers integral formula (Rogers [Acta Math. 94 (1955), 249–287]) to the adeles of number fields. We also prove the second moment formulas for a few important cases, enabling a number of classical and recent applications of the formula to extend immediately to any number field.
Seungki Kim
wiley   +1 more source

Addition formulas for Jacobi theta functions, Dedekind's eta function, and Ramanujan's congruences [PDF]

Pacific Journal of Mathematics, 2009
The author proves some new theta function identities, as well as series expansions for particular powers of Dedekind's eta function. As corollaries, known Ramanujan-type congruences for the partition function are derived.
openaire   +1 more source