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The number of integer points in a family of anisotropically expanding domains
number of integer points family of anisotropically expanding domains Number Theory
2012/4/17
We investigate the remainder in the asymptotic formula for the number of integer points in a family of bounded domains in the Euclidean space, which remain unchanged along some linear subspace and exp...
A binomial identity on the least prime factor of an integer
binomial identity least prime factor of an integer Number Theory
2011/9/22
Abstract: An identity for binomial symbols modulo an odd positive integer $n$ relating to the least prime factor of $n$ is proved. The identity is discussed within the context of Pell conics.
An Elliptic Analogue Of Generalized Cotangent Dirichlet Series And Its Transformation Formulae At Some Integer Arguments
Elliptic Analogue Cotangent Dirichlet Series Integer Arguments Number Theory
2011/9/20
Abstract: B.C. Berndt evaluated special values of the cotangent Dirichlet series. T. Arakawa studied a generalization of the series, or generalized cotangent Dirichlet series, and gave its transformat...
On the degree of a Kloosterman sum as an algebraic integer
cyclotomic field Kloosterman sum
2011/8/22
Abstract: The maximal degree over rational numbers that an n-dimensinonal Kloosterman sum defined over a finite field of characteristic p can achieve is known to be (p-1)/d where d=gcd(p-1,n+1). Wan h...
Given a matrix A 2 Zm×n satisfying certain regularity assumptions,a well-known integer programming problem asks to find an integer point in the associated knapsack polytope
P(A, b) = {x 2 Rn 0 : Ax ...
For a given positive integer $m$, let $A=\set{0,1,\ldots,m}$ and $q \in (m,m+1)$. A sequence $(c_i)=c_1c_2 \ldots$ consisting of elements in $A$ is called an expansion of $x$ if $\sum_{i=1}^{\infty} c...
We define a new sequence of positive integers, associated with Catalan numbers and Narayana polynomials.
Thue-Morse at Multiples of an Integer
Thue-Morse sequence sum of digits congruences arithmetic progressions
2010/12/14
Let t = (tn)n0 be the classical Thue-Morse sequence defined
by tn = s2(n) mod 2, where s2 is the sum of the bits in the binary repre-sentation of n. It is well known that for any integer k ≥ 1 the f...