Mathematicians crack hidden patterns in abstract number systems
Researchers have solved a decades-old mathematical puzzle about how to compute properties of exotic number structures used in cryptography and coding theory. The breakthrough delivers concrete formulas and algorithms that could accelerate computational work in fields relying on these abstract systems, from secure communications to data validation.
Originaltitel: Traces of Hecke operators on Drinfeld modular forms for GL2(Fq[T])
Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case . We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree. We improve the Ramanujan bound and deduce the decomposition of cusp forms of level into oldforms and newforms, as conjectured by Bandini–Valentino, under the hypothesis that each Hecke eigenvalue has multiplicity less than .