Related papers: Products of Factorials Modulo p

We study integral ratios of hook products of quotient partitions. This question is motivated by an analogous question in number theory concerning integral factorial ratios. We prove an analogue of a theorem of Landau that already applied in…

We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial P(T) modulo l. As an application we find the proportion of isogeny classes of abelian varieties with a…

A classification of the ways in which an element of a free group can be expressed as a product of commutators or as a product of squares is given. This is then applied to some particular classes of elements. Finally, a question about…

We construct the moduli stack of torsors over the formal punctured disk in characteristic p > 0 for a finite group isomorphic to the semidirect product of a p-group and a tame cyclic group. We prove that the stack is a limit of separated…

A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non…

We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely generated residually finite group. The same holds for Cartesian producs of other simple groups…

Let $p \equiv 1 \pmod{4}$ be prime, let $m$ and $n$ be integers such that $p=m^2+n^2$, and let $b$ be a positive integer. Let $Q(z,q) = (z,q/z,q;q)_{\infty}(qz^2,q/z^2;q^2)_{\infty}$ denote the product appearing in the quintuple product…

This is a study of universal problems for semimodules, in particular coequalizers, coproducts, and tensor products. Furthermore the structure theory of semiideals of the semiring of natural numbers is extended.

We primarily investigate congruences modulo $p$ for finite sums of the form $\sum_k\binom{rk}{k}x^k/k$ over the ranges $0<k<p$ and $0<k<p/r$, where $p$ is a prime larger than the positive integer $r$. Here $x$ is an indeterminate, thus…

We study right exact tensor products on the category of finitely presented functors. As our main technical tool, we use a multilinear version of the universal property of so-called Freyd categories. Furthermore, we compare our constructions…

We investigate the structure of the $p$-divisor for the Jouanolou foliation where we show, under some conditions, that it can be irreducible or has a $p$-factor. We study the reduction modulo $p$ of foliations on the projective plane and…

We show that, under fairly general conditions, many elements of a p-adic group can be well approximated by a product whose factors have properties that are helpful in performing explicit character computations.

In this paper we initiate a study on Gauss factorials of polynomials over finite fields, which are the analogues of Gauss factorials of positive integers.

We construct the tensor product for f-algebras, including proving a universal property for it, and investigate how it preserves algebraic properties of the factors.

We consider multiplication properties of elements in weighted Fourier Lebesgue and modulation spaces. Especially we extend some results by Pilipovic, Teofanov and Toft (2010).

This is my talk on the Bourbaki seminar, November 1996. It contains an elementary introduction to Borcherds' product formulas.

We investigate the interaction between the product of invariant types and domination-equivalence. We present a theory where the latter is not a congruence with respect to the former, provide sufficient conditions for it to be, and study the…

In this paper, we study primeness and pseudo primeness of p-adic meromorphic functions. We also consider left (resp. right ) primeness of these functions. We give, in particular, sufficient conditions for a meromorphic function to satisfy…

We prove that every finite dimensional representation of a finite group over a field of characteristic p admits a finite resolution by p-permutation modules. The proof involves a reformulation in terms of derived categories.

We study the problem when every matrix over a division ring is representable as either the product of traceless matrices or the product of semi-traceless matrices, and also give some applications of such decompositions. Specifically, we…