Anna Haensch

Almost Universal Ternary Sums of Squares and Triangular Numbers

For any integer x, let T x denote the triangular number \(\frac{x(x+1)} {2}\). In this paper we give a complete characterization of all the triples of positive integers (α, β, γ) for which the ternary sums \(\alpha {x}^{2} +\beta T_{y} +\gamma T_{z}\) represent all but finitely many positive integers. This resolves a conjecture of Kane and Sun (Trans Am Math Soc 362:6425–6455, 2010, Conjecture 1.19(i)) and complete the characterization of all almost universal ternary mixed sums of squares and triangular numbers.

Primitive Prime Divisors in Zero Orbits of Polynomials

Abstract. Let be a sequence of integers. A primitive prime divisor of a term is a prime which divides but does not divide any of the previous terms of the sequence. A zero orbit of a polynomial is a sequence of integers where the n-th term is the n-th iterate of at 0. We consider primitive prime divisors of zero orbits of polynomials. In this note, we show that for in , where and , every iterate in the zero orbit of contains a primitive prime divisor whenever zero has an infinite orbit. If , then every iterate after the first contains a primitive prime divisor.

Almost universal ternary sums of polygonal numbers

For a natural number m, generalized m-gonal numbers are those numbers of the form

Kneser–Hecke-Operators for Codes over Finite Chain Rings

p_m(x)=\frac{(m-2)x^2-(m-4)x}{2}

A characterization of almost universal ternary quadratic polynomials with odd prime power conductor

pm(x)=(m-2)x2-(m-4)x2 with

Completeness of the list of spinor regular ternary quadratic forms

x\in \mathbb Z