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Invariant Differential Operators on Siegel-Jacobi Space
invariants invariant differential operators Siegel-Jacobi space
2011/8/24
Abstract: For two positive integers $m$ and $n$, we let ${\mathbb H}_n$ be the Siegel upper half plane of degree $n$ and let ${\mathbb C}^{(m,n)}$ be the set of all $m\times n$ complex matrices. In th...
A mean value formula for elliptic curves
elliptic curves Weierstrass ℘ -function point multiplication division polynomial
2011/8/24
Abstract: It is proved in this paper that for any point on an elliptic curve, the mean value of x-coordinates of its n-division points is the same as its x-coordinate and that of y-coordinates of its ...
Ehrhart's polynomial for equilateral triangles in $\mathbb Z^3$
Ehrhart polynomial linear Diophantine equations lattice points equilateral triangles sequences regular integral polytopes
2011/8/25
Abstract: In this paper we calculate the Ehrhart's polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in $\mathbb Z^3$. The polynomial takes a relatively simple f...
Ramanujan Invariants for discriminants congruent to $\mathbf{5\;mod \;24
Ramanujan Invariants discriminants Number Theory
2011/8/23
Abstract: In this paper we compute the minimal polynomials of Ramanujan values $27t_n^{-12}$ for discriminants D\equiv5mod24. Our method is based on Shimura Reciprocity Law as which was made computati...
Abstract: In this paper we prove new upper bounds for the sum $\sum_{n=a+1}^{a+N}f(n)$, for a certain class of arithmetic functions $f$. Our results improve the previous results of G. Bachman and L. R...
Numerically explicit version of the Pólya--Vinogradov inequality
Numerically explicit version the Pólya--Vinogradov inequality
2011/8/23
Abstract: In this paper we proved a new numerically explicit version of the P\'{o}lya--Vinogradov inequality. Our proof is based on the new ideas of V.A. Bykovskii and improves a recent inequality obt...
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...
Heuristics on pairing-friendly elliptic curves
Elliptic curves finite fields pairing-based cryptography
2011/8/23
Abstract: We present a heuristic asymptotic formula as $x\to \infty$ for the number of pairing-friendly elliptic curves with fixed embedding degree $k\geq 3$, with fixed discriminant, with rho-value b...
A simple proof of Sarkozy's theorem
Sarkozy's theorem Number Theory Classical Analysis and ODEs
2011/8/23
Abstract: It is a striking and elegant fact (proved independently by Furstenberg and Sarkozy) that in any subset of the natural numbers of positive upper density there necessarily exist two distinct e...
On the distribution of cubic exponential sums
Exponential sums Cubic theta functions Metaplectic forms
2011/8/23
Abstract: Using the theory of metaplectic forms,we study the asymptotic behavior of cubic exponential sums over the ring of Eisenstein integers. In the first part of the paper, some non-trivial estima...
Operations on polytopes: application to tolerance analysis
Three dimensional Dimension Chain Geometric Specification Contact Specification Functional Requirement Polytope Tolerance.
2011/9/29
This article presents numerical methods in order to solve problems of tolerance analysis. A geometric specification, a contact specification and a functional
requirement can be respectively character...
Perturbation approach to multifractal dimensions for certain critical random matrix ensembles
multifractal dimensions Perturbation random matrix ensembles
2011/7/6
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain e...
Limits on the Stretch of Non-adaptive Constructions of Pseudo-Random Generators
Limits Non-adaptive Constructions Pseudo-Random Generators
2012/12/3
The standard approach for constructing a large-stretch pseudo-randomgenerator given a one-way permutation or given a smallerstretch pseudo-randomgenerator involves repeatedly composing the given primi...
An invariant in shock clustering and Burgers turbulence
Shock clustering stochastic coalescence kinetic theory Burgers turbulence integrable systems Loitsiansky invariant
2011/7/6
1-D scalar conservation laws with convex flux and Markov initial data
are now known to yield a completely integrable Hamiltonian system. In
this article, we rederive the analogue of Loitsiansky’s in...
Classification of Kac representations in the logarithmic minimal models LM(1,p)
Classification of Kac representations logarithmic minimal models LM(1,p)
2011/3/3
For each pair of positive integers r, s, there is a so-called Kac representation (r, s) associated with a Yang-Baxter integrable boundary condition in the lattice approach to the logarithmic minimal m...