The problem of phase retrieval is a difficult one which remains far from solved. Two homometric sets are always connected by way of a convolution product by some spectral unit, though not necessarily in a unique way. Here we elucidate one small aspect, the subgroup of spectral units with finite order. Its elements are completely characterized by relations between their eigenvalues. This sheds s...

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group O3 on the space R[x, y, z]2d of ternary forms of even degree 2d. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup B3 of signed...

This motivating question is lifted almost verbatim from B. Wyman’s 1972 article, [Wym72], of which the present article is merely an updated version. It may surprise the reader to learn that a large swath of modern number theory known as the Langlands program is dedicated to variations on the theme of Question A. We ought to clarify what is meant by a “rule” in Question A. We are not looking for...

In this chapter, we conduct a comparative study of various traders following different trading strategies. We design an agent-based artificial stock market consisting of two opposing types of traders: “rational traders” (or “fundamentalists”) and “imitators” (or “chartists”). Rational traders trade by trying to optimize their short-term income. On the other hand, imitators trade by copying the ...

To explain why the depressive realism effect has been found in trivial, artificial laboratory but not in more realistic or emotionally engaging situations, the authors hypothesized that depressed people overcompensate for a tendency toward maladaptive experiential (intuitive) processing by exercising excessive rational control in trivial situations. In more consequential situations, they are un...

By the Mordell-Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎There is no known algorithm for finding the rank of this group‎. ‎This paper computes the rank of the family $ E_p:y^2=x^3-3px $ of elliptic curves‎, ‎where p is a prime‎.

we discuss whether finiteness properties of a profinite group $g$ can be deduced from the coefficients of the probabilisticzeta function $p_g(s)$. in particular we prove that if $p_g(s)$ is rational and all but finitely many non abelian composition factors of $g$ are isomorphic to $psl(2,p)$ for some prime $p$, then $g$ contains only finitely many maximal subgroups.