Results 51 to 60 of about 229 (136)

A Cusp Form Example as An Eta Product

, 2022
Modular forms are important in several branches of mathematics especially in number theory and they have interesting properties. For example, they have lots of internal symmetries and they are finite vector spaces over complex field.
Avcı, Uygar, İnam, İlker, Demirkol Özkaya, Zeynep   +2 more
core  

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

Class invariants from a new kind of Weber-like modular equation [PDF]

A technique is described for explicitly evaluating quotients of the Dedekind eta function at quadratic integers. These evaluations do not make use of complex approximations but are found by an entirely `algebraic' method.
Hart, William B.
core  

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

Boundedness in families with applications to arithmetic hyperbolicity

Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.
Abstract Motivated by conjectures of Demailly, Green–Griffiths, Lang and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to show the persistence of arithmetic hyperbolicity along field extensions for projective normal surfaces with non‐zero irregularity.
Raymond van Bommel, Ariyan Javanpeykar, Ljudmila Kamenova   +2 more
wiley   +1 more source

Modular cocycles and linking numbers [PDF]

, 2017
It is known that the 3-manifold SL(2, Z) \ SL(2, R) is diffeomorphic to the complement of the trefoil knot in S-3. E. Ghys showed that the linking number of this trefoil knot with a modular knot is given by the Rademacher symbol, which is a ...
W. Duke, Duke, W., Imamoḡlu, Ö., Ö. Imamoḡlu, Á. Tóth, Tóth, Á.   +5 more
core   +1 more source