A Spanning Set and Potential Basis of the Mixed Hecke Algebra on Two Fixed Strands
Sign Up to like & getrecommendations! Published in 2017 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-018-1240-7
Abstract: The mixed braid groups $$B_{2,n}, \ n \in \mathbb {N}$$B2,n,n∈N, with two fixed strands and n moving ones, are known to be related to the knot theory of certain families of 3-manifolds. In this paper,… read more here.
Keywords: two fixed; mixed hecke; basis; fixed strands ... See more keywords
Comparing Hecke eigenvalues of newforms
Sign Up to like & getrecommendations! Published in 2017 at "Archiv der Mathematik"
DOI: 10.1007/s00013-017-1072-x
Abstract: Given two distinct newforms with real Fourier coefficients, we show that the set of primes where the Hecke eigenvalues of one of them dominate the Hecke eigenvalues of the other has density $$\ge $$≥1/16. Furthermore,… read more here.
Keywords: hecke eigenvalues; hecke; comparing hecke; eigenvalues newforms ... See more keywords
Cyclotomic Yokonuma–Hecke algebras are cyclotomic quiver Hecke algebras
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2017.03.004
Abstract: We prove that cyclotomic Yokonuma–Hecke algebras of type A are cyclotomic quiver Hecke algebras and we give an explicit isomorphism with its inverse, using a similar result of Brundan and Kleshchev on cyclotomic Hecke algebras.… read more here.
Keywords: hecke algebras; algebras cyclotomic; hecke; cyclotomic quiver ... See more keywords
A categorification of Hecke algebras with parameters 1 and v
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2019.06.031
Abstract: We categorify the Hecke algebra with parameters 1 and v using a variation of the category of Soergel bimodules. read more here.
Keywords: hecke algebras; hecke; categorification hecke; algebras parameters ... See more keywords
On graphs of Hecke operators
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2018.11.009
Abstract: Abstract The graph of a Hecke operator encodes all information about the action of this operator on automorphic forms. Let X be a curve over F q , F its function field and A the… read more here.
Keywords: hecke; graphs hecke; hecke operators;
The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2018.12.002
Abstract: Let $f$ and $g$ be two distinct newforms with weights $k_1, k_2 \ge 2$ and square-free levels $N_1, N_2 \ge 1$ respectively and which are normalized Hecke eigenforms. Further, for $n\ge 1$, let $ a_f(n)$… read more here.
Keywords: hecke; sequence; sign change; non vanishing ... See more keywords
Application of automorphic forms to lattice problems
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Cryptology"
DOI: 10.1515/jmc-2021-0045
Abstract: Abstract In this article, we propose a new approach to the study of lattice problems used in cryptography. We specifically focus on module lattices of a fixed rank over some number field. An essential question… read more here.
Keywords: forms lattice; lattice problems; number; hecke ... See more keywords