Related papers: An exact geometric mass formula

The main focus of this paper is on the problem of relating an ideal $I$ in the polynomial ring $\mathbb Q[x_1, \dots, x_n]$ to a corresponding ideal in $\mathbb F_p[x_1,\dots, x_n]$ where $p$ is a prime number; in other words, the…

We prove a Cherednik style $p$-adic uniformization theorem for Shimura varieties associated to certain groups of unitary similitudes of size two over totally real fields. Our basic tool is the alternative modular interpretation of the…

Let $G$ be a finite group and let $p$ be a prime. In this paper, we study the structure of finite groups with a large number of $p$-regular conjugacy classes or, equivalently, a large number of irreducible $p$-modular representations. We…

This is a complete classification of the complex forms of quaternionic symmetric spaces

We outline a general method for obtaining exact solutions of Schr\"{o}dinger equations with a position dependent effective mass and compare the results with those obtained within the frame of supersymmetric quantum theory. We observe that…

We establish an analogue of the classical Polya-Vinogradov inequality for $GL(2, \F_p)$, where $p$ is a prime. In the process, we compute the `singular' Gauss sums for $GL(2, \F_p)$. As an application, we show that the collection of…

Let $p$ be an odd prime, let $n\ge2$, and let the $n$th Chebyshev polynomial $T_n$ act on $\Z/p^k\Z$. We count fixed and exact-periodic points, allowing non-permutation degrees, and organize the finite-field formulas by the two source…

We prove congruences, modulo a power of a prime p, for certain finite sums involving central binomial coefficients $\binom{2k}{k}$.

We introduce extremely symmetric primes and provide some elementary properties of these.

In the previous article, we classified the characters associated to algebraic points on Shimura curves of $\Gamma_0(p)$-type, and over a quadratic field we showed that there are at most elliptic points on such a Shimura curve for every…

To obtain the most accurate predictions for the Higgs masses in the minimal supersymmetric model (MSSM), one should compute the full set of one-loop radiative corrections, resum the large logarithms to all orders, and add the dominant…

This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…

In this we give a detailed proof of fermionic p-adic q-measures on Z_p and we will treat some interesting formulae related q-extension of Euler numbers and polynomials.

We introduce a division formula on a possibly singular projective subvariety $X$ of complex projective space $\Pk^N$, which, e.g., provides explicit representations of solutions to various polynomial division problems on the affine part of…

This article introduces two reduction schemes for Hamiltonian systems on an exact symplectic manifold admitting Lie group symmetries. It is demonstrated that these reduction procedures are equivalent by employing a modified…

We prove a fixed point theorem for the action of certain local monodromy groups on \'etale covers and use it to deduce lower bounds in essential dimension. In particular, we give more geometric proofs of many (but not all) of the results of…

We provide conditions on the p-adic Galois representation of a smooth proper variety over a complete nonarchimedean extension of Q_p to have (potentially) good ordinary reduction.

We prove a positive mass theorem for complete K\"ahler manifolds that are asymptotic to the complex hyperbolic space.

We discuss the fermion mass problem in SUSY GUTs, including such ideas as texture zeroes, and Georgi-Jarlskog textures. We focus on a specific supersymmetric model based on the gauge group $SU(4)\otimes SU(2)_L \otimes SU(2)_R$. In this…

Let p be a prime = 3 (mod 4). A number of elegant number-theoretical properties of the sums T(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} tan(n^2\pi/p) and C(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} cot(n^2\pi/p) are proved. For example, T(p) equals p times…