We develop a simple algebraic approach to the study of the Weil representation associated to a finite abelian group. As a result, we obtain a simple proof of a generalisation of a well-known formula for the absolute value of its character. We also obtain a new result about its decomposition into irreducible representations. As an example, the decomposition of the Weil representation of Sp2g(Z/N...

Integer Programming Cláudio N. Meneses Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, Florida, 32611, USA, [email protected] Zhaosong Lu School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA, [email protected] Carlos A.S. Oliveira, Panos M. Pardalos Department of Industrial and S...

The idea is that the equality of the Euler product and Riemann-Hadamard product for zeta allows extraction of an exact formula for a suitably-weighted counting of primes, a sum over zeros of zeta, via a contour integration of the logarithmic derivatives. As observed by [Guinand 1947] and [Weil 1952], [Weil 1972], the classical formulas are equalities of values of a certain distribution, in the ...

A. Weil proved that the geometric Frobenius π = Fa of an abelian variety over a finite field with q = pa elements has absolute value √ q for every embedding. T. Honda and J. Tate showed that A 7→ πA gives a bijection between the set of isogeny classes of simple abelian varieties over Fq and the set of conjugacy classes of q-Weil numbers. Higher-dimensional varieties over finite fields, Summer s...

For every prime p we give infinitely many examples of torsors under abelian varieties over Q that are locally trivial but not divisible by p in the Weil-Châtelet group. We also give an example of a locally trivial torsor under an elliptic curve over Q which is not divisible by 4 in the Weil-Châtelet group. This gives a negative answer to a question of Cassels.

Very rough notes for a lecture to be given October 5, 2013 at the Quebec/Maine Number Theory Conference. I’ll discuss diophantine questions that take on a somewhat different flavor when one deals with varying number fields rather than restricts to Q as a base field: an on-going joint project with Maarten Derickx and Sheldon Kamienny regarding Mordell-Weil torsion, and some recent work with Zev ...

MATHIEU DECLERCK and JUDIT KORMOS Bilingualism: Language and Cognition / Volume 15 / Issue 04 / October 2012, pp 782 ­ 796 DOI: 10.1017/S1366728911000629, Published online: 04 January 2012 Link to this article: http://journals.cambridge.org/abstract_S1366728911000629 How to cite this article: MATHIEU DECLERCK and JUDIT KORMOS (2012). The effect of dual task demands and proficiency on second lan...

To provide an overview of leptospirosis in Queensland, the World Health Organization/Food and Agriculture Organization Collaborating Centre for Reference and Research on Leptospirosis undertook a study of notifications of the disease from 1985 to 1996. The review encompassed information drawn from notifications to Queensland Health and questionnaires sent to doctors. Notifications were highest ...

We determine all complex K3 surfaces with Picard rank 20 over Q. Here the NéronSeveri group has rank 20 and is generated by divisors which are defined over Q. Our proof uses modularity, the Artin-Tate conjecture and class group theory. With different techniques, the result has been established by Elkies to show that Mordell-Weil rank 18 over Q is impossible for an elliptic K3 surface. We also a...

An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable in H(X;Z)∪H(X;Z) ⊂ H(X;Z). One of the features of this special case is that the corresponding Azumaya bundle can be realized in terms of smoothing operators. The topological and the analytic index of a projective family of elliptic operators...