We explicate the combinatorial/geometric ingredients of Arthur’s proof of the convergence and polynomiality, in a truncation parameter, of his noninvariant trace formula. Starting with a fan in a real, finite dimensional, vector space and a collection…
Let
be squarefree with
. Let
denote the number of N-colored generalized Frobenius partitions of n introduced by Andrews in 1984, and
denote the number of partitions of n. We prove
where
is a cusp form in
. This e…
We obtain a nontrivial upper bound for the multiplicative energy of any sufficiently large subset of a subvariety of a finite algebraic group. We also find some applications of our results to the growth of conjugates classes, estimates of exponential…
The notion of the truncated Euler characteristic for Iwasawa modules is a generalization of the the usual Euler characteristic to the case when the Selmer groups are not finite. Let p be an odd prime,
and
be elliptic curves over a number …
We study the free metabelian group
of prime power exponent n on two generators by means of invariants
that we construct from colorings of the squares in the integer grid
. In particular, we improve bounds found by Newman for the orde…
Let G be a simple complex algebraic group, and let
be a reductive subgroup such that the coordinate ring of
is a multiplicity-free G-module. We consider the G-algebra structure of
and study the decomposition into irreducible summands…
We study the number of ways of factoring elements in the complex reflection groups
as products of reflections. We prove a result that compares factorization numbers in
to those in the symmetric group
, and we use this comparison, along …
We study families of metrics on automorphic vector bundles associated with representations of the modular group. These metrics are defined using an Eisenstein series construction. We show that in certain cases, the residue of these Eisenstein metrics…
The cardinal invariant
is defined as the minimum size of a family of
-monochromatic sets that cover
(where
is the parity of the biggest initial segment both x and y have in common). We prove that
holds in Shelah’s model of…
We give a formula for the cohomological invariants of a root stack, which we apply to compute the cohomological invariants and the Brauer group of the compactification of the stacks of hyperelliptic curves given by admissible double coverings.