A generalization of Perron's theorem about Hurwitzian numbers
A generalization of Pillai's arithmetical function involving regular convolutions
A generalization of Proth's theorem
A generalization of Rademacher's reciprocity law
We generalize Rademacher's reciprocity formula for the Dedekind sum to a family of cotangent sums. One of the sums in this family is strictly related to the Vasyunin sum, a function defined on the rationals that is relevant to the Nyman-Beurling-Báez-Duarte approach to the Riemann hypothesis.
A generalization of Scholz’s reciprocity law
We provide a generalization of Scholz’s reciprocity law using the subfields and of , of degrees and over , respectively. The proof requires a particular choice of primitive element for over and is based upon the splitting of the cyclotomic polynomial over the subfields.
A generalization of some results in additive number theory.
A generalization of Stirling numbers of the second kind via a special multiset.
A generalization of Sturmian sequences: Combinatorial structure and transcendence
A generalization of Sylvester's and Frobenius' problems on numerical semigroups
A generalization of the Bernoulli polynomials.
A generalization of the binomial interpolated operator and its action on linear recurrent sequences.
A generalization of the Buchstab equation.
A generalization of the Chowla-Selberg formula.
A generalization of the classical circle problem
A generalization of the Goldbach-Vinogradov theorem
A generalization of the Hasse-Arf theorem.
A generalization of the Lerch-Mordell formulas for positive discriminants
A generalization of the LLL-algorithm over euclidean rings or orders
Numerous important lattices (, the Coxeter-Todd lattice , the Barnes-Wall lattice , the Leech lattice , as well as the -modular -dimensional lattices found by Quebbemann and Bachoc) possess algebraic structures over various Euclidean rings, e.g. Eisenstein integers or Hurwitz quaternions. One obtains efficient algorithms by performing within this frame the usual reduction procedures, including the well known LLL-algorithm.
A generalization of the method of global relation.
A generalization of the question of Sierpiński on geometric progressions.