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Discretization of prime counting functions, convexity and the Riemann hypothesis

Emre Alkan (2023)

Czechoslovak Mathematical Journal

We study tails of prime counting functions. Our approach leads to representations with a main term and an error term for the asymptotic size of each tail. It is further shown that the main term is of a specific shape and can be written discretely as a sum involving probabilities of certain events belonging to a perturbed binomial distribution. The limitations of the error term in our representation give us equivalent conditions for various forms of the Riemann hypothesis, for classical type zero-free...

Discriminant algebras and adjoints of quadratic forms.

Loos, Ottmar (1997)

Beiträge zur Algebra und Geometrie

Discriminants of certain algebraic number fields.

Kenzo Komatsu (1976)

Journal für die reine und angewandte Mathematik

Discriminants of Chebyshev radical extensions

T. Alden Gassert (2014)

Journal de Théorie des Nombres de Bordeaux

Let $t$ be any integer and fix an odd prime $ℓ$ . Let $Φ (x) = T_{ℓ}^{n} (x) - t$ denote the $n$ -fold composition of the Chebyshev polynomial of degree $ℓ$ shifted by $t$ . If this polynomial is irreducible, let $K = ℚ (θ)$ , where $θ$ is a root of $Φ$ . We use a theorem of Dedekind in conjunction with previous results of the author to give conditions on $t$ that ensure $K$ is monogenic. For other values of $t$ , we apply a result of Guàrdia, Montes, and Nart to obtain a formula for the discriminant of $K$ and compute an integral basis for the ring of integers...

Discriminants of etale algebras and related structures.

William C. Waterhouse (1987)

Journal für die reine und angewandte Mathematik

Discriminants of number fields defined by trinomials

P. Llorente, E. Nart, N. Vila (1984)

Acta Arithmetica

Disjoint Beatty sequences.

Simpson, Jamie (2004)

Integers

Disjoint covering systems and product-invariant relations

Ivan Korec (1985)

Mathematica Slovaca

Disjoint covering systems with precisely one multiple modulus

Marc Berger, Alexander Felzenbaum, Aviezri Fraenkel (1988)

Acta Arithmetica

Disjoint sequences in Boolean algebras

Ján Jakubík (1998)

Mathematica Bohemica

We deal with the system $Conv B$ of all sequential convergences on a Boolean algebra $B$ . We prove that if $α$ is a sequential convergence on $B$ which is generated by a set of disjoint sequences and if $β$ is any element of $Conv B$ , then the join $α \lor β$ exists in the partially ordered set $Conv B$ . Further we show that each interval of $Conv B$ is a Brouwerian lattice.