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Newton representation of functions over natural integers having integral difference ratios
[article]

2013
*
arXiv
*
pre-print

*Different*questions lead to the same class

*of*

*functions*from

*natural*

*integers*to

*integers*: those which

*have*

*integral*

*difference*

*ratios*, i.e. verifying f(a)-f(b)≡0 (a-b) for all a>b. ... We characterize this class

*of*

*functions*via their

*representations*as

*Newton*series. ...

*Newton*series

*of*

*functions*N → Z and

*integral*

*difference*

*ratios*Definition 2.1 (

*Newton*

*representation*for

*functions*N → Z). ...

##
###
Newton representation of functions over natural integers having integral difference ratios

2015
*
International Journal of Number Theory
*

*Different*questions lead to the same class

*of*

*functions*from

*natural*

*integers*to

*integers*: those which

*have*

*integral*

*difference*

*ratios*, i.e. verifying We characterize this class

*of*

*functions*via their ...

*representations*as

*Newton*series. ...

*Newton*series

*of*

*functions*N → Z and

*integral*

*difference*

*ratios*Definition 2.1 (

*Newton*

*representation*for

*functions*N → Z). ...

##
###
Generalized Kummer congruences and p-adic families of motives
[article]

1995
*
arXiv
*
pre-print

We describe some new general constructions

arXiv:math/9503218v1
fatcat:avkld77t3jgmzca3tddqszhfbu
*of*p-adic L-*functions*attached to certain arithmetically defined complex L-*functions*coming from motives*over*Q with coefficiens in a number field T, with [T: ... These constructions are equivalent to proving some generalized Kummer congruences for critical special values*of*these complex L-*functions*. ... The important condition*of*motives M P*of*the above family is that they*have*the same fixed p-invariant h = h P (generalized slope), which is defined as the*difference*between the*Newton*polygon and the ...##
###
Computing Bits of Algebraic Numbers
[article]

2011
*
arXiv
*
pre-print

a succinct (binary)

arXiv:1112.4295v1
fatcat:ji3l6p4ysrexrjy3dffq6gpjme
*representation*. ... The proof*of*our main result is entirely elementary, preferring to use the elementary Liouville's theorem*over*the much deeper Roth's theorem for algebraic numbers. ... We also thank anonymous referees*of*STACS 2012 for pointing out an error in the previous version and various stylistic improvements. ...##
###
Expressions for the Entropy of Binomial-Type Distributions
[article]

2018
*
arXiv
*
pre-print

As a result, we derive series expansions and

arXiv:1708.06394v4
fatcat:glu5koyecraejekd2m6qfodxgy
*integral**representations**of*the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, negative binomial, and hypergeometric ... Our results also establish connections between the entropy*functions*and to the Riemann zeta*function*and its generalizations. ... Using (4), we can immediately write down an*integral**representation**of*E Bin (n, p): E Bin (n, p) = ∞ 0 npe −t t − e −t (1 − (1 − p + pe −t ) n ) t(1 − e −t ) dt, so that we*have*the*integral**representation*...##
###
Hypergeometric Series Representations of Feynman Integrals by GKZ Hypergeometric Systems
[article]

2019
*
arXiv
*
pre-print

By applying the results

arXiv:1910.08651v1
fatcat:y2dkix6evbetdafsgpk3itptai
*of*Gelfand-Kapranov-Zelevinsky (GKZ) we derive a formula for a class*of*hypergeometric series*representations**of*Feynman*integrals*, which can be obtained by triangulations*of*the ... We show that almost all Feynman*integrals*as well as their coefficients in a Laurent series in dimensional regularization can be written in terms*of*Horn hypergeometric*functions*. ... Acknowledgements: This research is supported by the International Max Planck Research School for Mathematical and Physical Aspects*of*Gravitation, Cosmology and ...##
###
Dimension types
[chapter]

1994
*
Lecture Notes in Computer Science
*

The algorithm exploits equational unification

doi:10.1007/3-540-57880-3_23
fatcat:upckjidxbve4npp3oer2j2eawi
*over*Abelian groups in addition to ordinary term unification. An implementation*of*the type system is described, extending the ML Kit compiler. ... This paper extends a strongly-typed programming language with a notion*of*dimension type. Our approach improves on previous proposals in that dimension types may be polymorphic. ... But in their system there are no "dimension constants" (our base dimensions) and equations are not necessarily*integral*, so Gaussian elimination is used to solve them. ...##
###
Artin conjecture for $p$-adic Galois representations of function fields

2018
*
Mathematical Research Letters
*

For a global

doi:10.4310/mrl.2018.v25.n1.a6
fatcat:nu4fp7cgajd5dhsi2xnyhjrbki
*function*field K*of*positive characteristic p, we show that Artin's entireness conjecture for L-*functions**of*geometric padic Galois*representations**of*K is true in a non-trivial p-adic disk ... In particular, we prove the non-rationality 1*of*the geometric unit root L-*functions*. ... For an*integer*j ≥ 0, let ϕ j denote the unit root σ-module on U coming from the slope j-part in the Hodge-*Newton*decomposition*of*ϕ. ...##
###
Echoing the extra dimension

2003
*
Nuclear Physics B
*

The Green's

doi:10.1016/j.nuclphysb.2003.10.011
fatcat:4ntq57qvcraxbgkbqlojqhjz3a
*function*has a form*of*the sum*of*contributions from large number*of*images due to the compactness*of*the fifth dimension. ... Additionally, a peculiar feature*of*the causal wave propagation in five dimensions (making a five-dimensional spacetime very much*different*from the familiar four-dimensional case) is that the entire region ... Sum*over*images*representation*The*integration**over*momentum in (2.10) includes the*integration**over*angles and the*integration**over*absolute value p*of*the 4-momentum. ...##
###
On the status of expansion by regions

2019
*
European Physical Journal C: Particles and Fields
*

We discuss the status

doi:10.1140/epjc/s10052-019-6653-3
fatcat:y3kkv74d2zfsbpb3u2znmm33xm
*of*expansion by regions, i.e. a well-known strategy to obtain an expansion*of*a given multiloop Feynman*integral*in a given limit where some kinematic invariants and/or masses*have*... certain scaling measured in powers*of*a given small parameter. ... [Authors' comment: This is theoretical work, so we*have*not used any data.] ...##
###
Exact p-adic computation in Magma

2020
*
Journal of symbolic computation
*

The intention is that this article will be

doi:10.1016/j.jsc.2020.08.005
fatcat:ukfr2dl7obho5hdkbv7st5lqai
*of*benefit to anyone wanting to implement similar*functionality*in other languages. ... This has the benefits*of*increasing user-friendliness and speeding up some computations, as well as forcibly producing provable results. ... Such a*function*can be said to be an exact*representation**of*a real number, because no two distinct real numbers*have*the same*representation*: for a sufficiently large precision k, the representing*functions*...##
###
The Representation of Time in Discrete Mechanics
[chapter]

2017
*
Boston Studies in the Philosophy of Science
*

Acknowledgements We wish to thank the participants

doi:10.1007/978-3-319-53725-2_9
fatcat:nee7qhiebrcsjhlc3ozgwppx2m
*of*the conference Time*of**Nature*,*Nature**of*Time for comments and discussion. ... We are most grateful to Christophe Bouton and Philippe Huneman for helpful comments on previous drafts*of*this paper. ... It is defined as the*integral**over*time*of*the Lagrangian L c*of*the system: S c = L c dt. ...##
###
Cocenters of p-adic groups, III: Elliptic and rigid cocenters
[article]

2017
*
arXiv
*
pre-print

In this paper, we show that the elliptic cocenter

arXiv:1703.00378v2
fatcat:uyhctesnsbg7tioi3jrlb6apga
*of*the Hecke algebra*of*a connected reductive group*over*a nonarchimedean local field is contained in the rigid cocenter. ... As applications, we prove the trace Paley-Wiener theorem and the abstract Selberg principle for mod-l*representations*. ... These are finite reductive groups andM is a Levi subgroup ofK sp , hence the*ratio*is an*integer*. ...##
###
Concept of the exponential law prior to 1900

1978
*
American Journal of Physics
*

The historical development

doi:10.1119/1.11512
fatcat:micapjsbjvebvnw6zf3vxzg2re
*of*a quantitative perception*of*the processes*of*exponential growth and decay is traced from its ancient origins through pre-20th century mathematical formulations and physical ... Exponential processes were among the earliest quantitative concepts to be mathematically formulated, and our modem understanding*of*them can be enhanced by historical perspective. ... In addition Napier interpolated between*integer*numbers*of*successive products, not by extraction*of*roots but by setting*differences*between elements in the arithmetic progression proportional to*ratios*...##
###
Efficient Correlation Matching for Fitting Discrete Multivariate Distributions with Arbitrary Marginals and Normal-Copula Dependence

2009
*
INFORMS journal on computing
*

variables

doi:10.1287/ijoc.1080.0281
fatcat:7fhix4ln3faijnhyqfwaocjnqq
*over*(0 1); then X is obtained by applying the inverse*of*the target marginal distribution*function*for each coordinate*of*U. ... We also characterize the asymptotic convergence rate*of*the*function*r (as a*function**of*) to the continuous-marginals limiting*function*, when the discrete marginals converge to continuous distributions ... With the*Newton*-Cotes rules (Stoer and Bulirsch 1980, §3 .1), the*integral**over*a b is approximated as a sum*of*approximations*of*the*integral**over*the pieces*of*a partition*of*a b (see below), and it ...
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