The twisted group ring isomorphism problem over fields

Twisted L-functions over number fields and Hilbert's eleventh problem

Let K be a totally real number field, π an irreducible cuspidal representation of GL2(K)\GL2(AK) with unitary central character, and χ a Hecke character of conductor q. Then L(1/2, π ⊗ χ) ≪ (Nq) 1 2 − 1 8 , where 0 6 θ 6 1/2 is any exponent towards the Ramanujan– Petersson conjecture (θ = 1/9 is admissible). The proof is based on a spectral decomposition of shifted convolution sums and a genera...

Twisted Fermat curves over totally real fields

Constacyclic Codes over Group Ring (Zq[v])/G

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

The isomorphism problem for circulant graphs via Schur ring theory

This paper concerns the applications of Schur ring theory to the isomorphism problem of circulant graphs (Cayley graphs over cyclic groups). A digest of the most important facts about Schur rings presented in the first sections provides the reader with agentie self-eontained introduction to this area. The developed machinery allows us to give proofs of two eonjectures (Zibin' 1975 and Toida 197...

The isomorphism problem for classes of computable fields

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out several examples. One motivation is to see wheth...