We show that if $$N \geq {\rm exp}({\rm exp} (k^{O(1)})))$$ , then any k-colouring of the primes are less than N contains a monochromatic solution to $$p_1 - p_2 = p_3 -1$$ .

By a result of Schur [J. Reine Angew. Math. 140 (1911), pp. 1–28], the entrywise product M ? N M \circ N</mml:annotatio...

This paper builds upon the work of Cline [C] and Donkin [D1] to describe explicit equivalences between some categories associated to the category of rational modules for a reductive group G and categories associated to the category of rational modules for a Levi subgroup H . As an application, we establish an Ext-transfer result from rational G-modules to rational H-modules. In case G = GLn, th...

We present a simple technique to compute moments of derivatives of unitary characteristic polynomials. The first part of the technique relies on an idea of Bump and Gamburd: it uses orthonormality of Schur functions over unitary groups to compute matrix averages of characteristic polynomials. In order to consider derivatives of those polynomials, we here need the added strength of the Generaliz...