The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

We introduce the intersection cohomology module of a matroid and prove that it satisfies
Poincaré duality, the hard Lefschetz theorem, and the Hodge–Riemann relations. As …

This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The
paper is a survey of recent developments in the theory of toric varieties, including new …

Mirror duality and string-theoretic Hodge numbers Page 1 Invent. math. 126, 183–203 (1996)
Mirror duality and string-theoretic Hodge numbers Victor V. Batyrev1;?, Lev A. Borisov2; ?? 1 …

This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

Hypergeometric functions have occupied a significant position in mathematics for over two
centuries. This monograph, by one of the foremost experts, is concerned with the Boyarsky …

Let C be a smooth projective curve over a discretely valued field K, defined by an affine
equation f (x, y)= 0. We construct a model of C over the ring of integers of K using a toroidal …

In this paper, we continue to develop the systematic decomposition theory [18] for the
generic Newton polygon attached to a family of zeta functions over finite fields and more …

We construct motives over the rational numbers associated with symmetric power moments
of Kloosterman sums, and prove that their L-functions extend meromorphically to the …

Let $\pi $ be a ${\rm SL}(3,\Bbb {Z}) $ Hecke-Maass cusp form. Let $\chi=\chi_1\chi_2 $ be a
Dirichlet character with $\chi_i $ primitive modulo $ M_i $. Suppose $ M_1 $, $ M_2 $ are …