We construct a natural family of rational functions Ψ̃m on a Hilbert modular surface from the classical j-invariant and its Hecke translates. These functions are obtained by means of a multiplicative analogue of the Doi-Naganuma lifting and can be viewed as twisted Borcherds products. We then study when the value of Ψ̃m at a CM point associated to a non-biquadratic quartic CM field generates the ...

Let K be a totally real number field of degree n. We show that the number of totally positive integers (or more generally the number of totally positive elements of a given fractional ideal) of given trace is evenly distributed around its expected value, which is obtained from geometric considerations. This result depends on unfolding an integral over a compact torus. Introduction In 1921 Hecke...

In this paper we discuss a coding and the associated symbolic dynamics for the geodesic flow on Hecke triangle surfaces. We construct an explicit cross section for which the first return map factors through a simple (explicit) map given in terms of the generating map of a particular continued fraction expansion closely related to the Hecke triangle groups. We also obtain explicit expressions fo...

Lusztig’s presentation of the graded Hecke algebra in terms of generators and relations allows for the definition of algebras associated to noncrystallographic root systems. The representation theory of general graded Hecke algebras is investigated, the expected number of tempered representations for H(H3) are accounted for, and it is shown that one of these representations has the unexpected p...

Let E(p) denote the Eisenstein ideal in the Hecke algebra T(p) of the Drinfeld modular curve X0(p) parameterizing Drinfeld modules of rank two over Fq[T ] of general characteristic with Hecke level p-structure, where p⊳ Fq[T ] is a nonzero prime ideal. We prove that the characteristic p of the field Fq does not divide the order of the quotient T(p)/E(p) and the Eisenstein ideal E(p) is locally ...

Abstract. We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to a congruence subgroup. Such an estimate has applications to the analytic theory of elliptic curves over a finite field, going beyond the Riemann hypothesis over finite fields. As the main tool to prove our bound on traces of Hecke operators, we develop a Petersson for...

We examine blocks of the Ariki–Koike algebra, in an attempt to generalise the combinatorial representation theory of the Iwahori–Hecke algebra of type A. We identify a particular type of combinatorial block, which we call a core block, which may be viewed as an analogue of a simple block of the Iwahori–Hecke algebra. We give equivalent characterisations of core blocks and examine their basic co...

The study of representations of aane Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any nite Coxeter group. This paper is completely independent of aane Hecke algebra theory and is purely combinatorial. We deene generalized shapes and standard Young tableaux and show that these new objects coincide with the classical ones for root...

1. Sunaert S, Van Oostende S, Van Hecke P, Marchal G and Orban GA. The kinetic occipital (KO) area of man: a functional MRI study. Belgian Society for Neuroscience, Brussels, 9-10 May, 1996.2. Van Oostende S, Sunaert S, Van Hecke P, Marchal G and Orban GA. Functional magnetic resonance imaging (fMRI) study of the human visual system: the kinetic occipital (KO) area. Joint Meeting of the Bel...