Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Concept

Divisor function

Related publications (14)

A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

Thomas Mountford

In this paper we use the Riemann zeta distribution to give a new proof of the Erdos-Kac Central Limit Theorem. That is, if zeta(s) = Sigma(n >= 1) (1)(s)(n) , s > 1, then we consider the random variable X-s with P(X-s = n) = (1) (zeta) ( ...

Amer Mathematical Soc2023

Singularities of general fibers and the LMMP

Zsolt Patakfalvi

We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by p - 1. We deduce ...

JOHNS HOPKINS UNIV PRESS2022

Logic Resynthesis of Majority-Based Circuits by Top-Down Decomposition

Giovanni De Micheli, Heinz Riener, Siang-Yun Lee

Logic resynthesis is the problem of finding a dependency function to re-express a given Boolean function in terms of a given set of divisor functions. In this paper, we study logic resynthesis of majority-based circuits, which is motivated by the increasin ...

IEEE2021

The Shifted Convolution of Generalized Divisor Functions

Berke Topacogullari

We prove an asymptotic formula for the shifted convolution of the divisor functions d(k)(n) and d(n) with k >= 4, which is uniform in the shift parameter and which has a power saving error term, improving results obtained previously by Fouvry and Tenenbaum ...

OXFORD UNIV PRESS2018

Imaging the Dynamics of Neocortical Population Activity in Behaving and Freely Moving Mammals

Carl Petersen

The development of functional imaging techniques applicable to neuroscience and covering a wide range of spatial and temporal scales has greatly facilitated the exploration of the relationships between cognition, behaviour and electrical brain activity. Fo ...

Springer-Verlag Berlin2015

Schizophrenia patients and 22q11.2 deletion syndrome adolescents at risk express the same deviant patterns of resting state EEG microstates: A candidate endophenotype of schizophrenia

Michael Herzog, Dimitri Nestor Alice Van De Ville, Maya Roinishvili, Maude Schneider, Fikret Isik Karahanoglu

Schizophrenia is a complex psychiatric disorder and many of the factors contributing to its pathogenesis are poorly understood. In addition, identifying reliable neurophysiological markers would improve diagnosis and early identification of this disease. T ...

2015

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Philippe Michel

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...

European Mathematical Soc2014

Computation Over Gaussian Networks With Orthogonal Components

Michael Christoph Gastpar, Chien-Yi Wang

Function computation over Gaussian networks with orthogonal components is studied for arbitrarily correlated discrete memoryless sources. Two classes of functions are considered: 1) the arithmetic sum function and 2) the type function. The arithmetic sum f ...

Institute of Electrical and Electronics Engineers2014

Computation over Gaussian networks with orthogonal components

Michael Christoph Gastpar, Chien-Yi Wang

Function computation of arbitrarily correlated discrete sources over Gaussian networks with multiple access components but no broadcast is studied. Two classes of functions are considered: the arithmetic sum function and the frequency histogram function. T ...

2013

Stable averages of central values of Rankin-Selberg L-functions: Some new variants

Paul David Nelson

As shown by Michel and Ramakrishnan (2007) and later generalized by Feigon and Whitehouse (2008), there are "stable" formulas for the average central L-value of the Rankin-Selberg convolutions of some holomorphic forms of fixed even weight and large level ...

Academic Press Inc Elsevier Science2013

Application of the Matrix Pencil Method to Rational Fitting of Frequency-Domain Responses

Farhad Rachidi-Haeri, Mario Paolone, Hamidreza Karami, Keyhan Sheshyekani

This paper presents a general methodology based on the matrix pencil method (MPM) for the fitting of frequency-domain responses in order to be properly represented in time-domain analysis. By virtue of the proposed method, a rational fitting of the frequen ...

Ieee-Inst Electrical Electronics Engineers Inc2012

Statistics Of Prime Divisors In Function Fields

We show that the prime divisors of a random polynomial in F-q[t] are typically "Poisson distributed". This result is analogous to the result in Z of Granville [1]. Along the way, we use a sieve developed by Granville and Soundararajan [2] to give a simple ...

2009

2-Selmer groups and the Birch-Swinnerton-Dyer Conjecture for the congruent number curves

We take an approach toward Counting the number of integers n for which the curve (n),: y(2) = x(3) - n(2)x has 2-Selmer groups of a given size. This question was also discussed in a pair of papers by Roger Heath-Brown. In contrast to earlier work, our anal ...

2009

Le carré de la fonction des diviseurs

Let d(n) denote Dirichlet's divisor function for positive integer numbers. This work is primarily concerned with the study of We are interested, in the error term where Ρ3 is a polynomial of degree 3 ; more precisely xΡ3(log x) is the residue of in s = 1. ...

EPFL2007