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

Patrick Cegielski, Serge Grigorieff, Irene Guessarian
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).  ... 
arXiv:1310.1507v1 fatcat:omm2c53r2jaonlyabak3q3dbjq

Newton representation of functions over natural integers having integral difference ratios

Patrick Cégielski, Serge Grigorieff, Irène Guessarian
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).  ... 
doi:10.1142/s179304211550092x fatcat:7okzicagrndl7htxhjjb6g42de

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

Alexei A. Panchishkin
1995 arXiv   pre-print
We describe some new general constructions 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  ... 
arXiv:math/9503218v1 fatcat:avkld77t3jgmzca3tddqszhfbu

Computing Bits of Algebraic Numbers [article]

Samir Datta, Rameshwar Pratap
2011 arXiv   pre-print
a succinct (binary) 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.  ... 
arXiv:1112.4295v1 fatcat:ji3l6p4ysrexrjy3dffq6gpjme

Expressions for the Entropy of Binomial-Type Distributions [article]

Mahdi Cheraghchi
2018 arXiv   pre-print
As a result, we derive series expansions and 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  ... 
arXiv:1708.06394v4 fatcat:glu5koyecraejekd2m6qfodxgy

Hypergeometric Series Representations of Feynman Integrals by GKZ Hypergeometric Systems [article]

René Pascal Klausen
2019 arXiv   pre-print
By applying the results 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  ... 
arXiv:1910.08651v1 fatcat:y2dkix6evbetdafsgpk3itptai

Dimension types [chapter]

Andrew Kennedy
1994 Lecture Notes in Computer Science  
The algorithm exploits equational unification 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.  ... 
doi:10.1007/3-540-57880-3_23 fatcat:upckjidxbve4npp3oer2j2eawi

Artin conjecture for $p$-adic Galois representations of function fields

Ruochuan Liu, Daqing Wan
2018 Mathematical Research Letters  
For a global 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.  ... 
doi:10.4310/mrl.2018.v25.n1.a6 fatcat:nu4fp7cgajd5dhsi2xnyhjrbki

Echoing the extra dimension

A.O. Barvinsky, Sergey N. Solodukhin
2003 Nuclear Physics B  
The Green's 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.  ... 
doi:10.1016/j.nuclphysb.2003.10.011 fatcat:4ntq57qvcraxbgkbqlojqhjz3a

On the status of expansion by regions

Tatiana Yu. Semenova, Alexander V. Smirnov, Vladimir A. Smirnov
2019 European Physical Journal C: Particles and Fields  
We discuss the status 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.]  ... 
doi:10.1140/epjc/s10052-019-6653-3 fatcat:y3kkv74d2zfsbpb3u2znmm33xm

Exact p-adic computation in Magma

Christopher Doris
2020 Journal of symbolic computation  
The intention is that this article will be 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  ... 
doi:10.1016/j.jsc.2020.08.005 fatcat:ukfr2dl7obho5hdkbv7st5lqai

The Representation of Time in Discrete Mechanics [chapter]

Vincent Ardourel, Anouk Barberousse
2017 Boston Studies in the Philosophy of Science  
Acknowledgements We wish to thank the participants 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.  ... 
doi:10.1007/978-3-319-53725-2_9 fatcat:nee7qhiebrcsjhlc3ozgwppx2m

Cocenters of p-adic groups, III: Elliptic and rigid cocenters [article]

Dan Ciubotaru, Xuhua He
2017 arXiv   pre-print
In this paper, we show that the elliptic cocenter 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.  ... 
arXiv:1703.00378v2 fatcat:uyhctesnsbg7tioi3jrlb6apga

Concept of the exponential law prior to 1900

Lorenzo J. Curtis
1978 American Journal of Physics  
The historical development 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  ... 
doi:10.1119/1.11512 fatcat:micapjsbjvebvnw6zf3vxzg2re

Efficient Correlation Matching for Fitting Discrete Multivariate Distributions with Arbitrary Marginals and Normal-Copula Dependence

Athanassios N. Avramidis, Nabil Channouf, Pierre L'Ecuyer
2009 INFORMS journal on computing  
variables 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  ... 
doi:10.1287/ijoc.1080.0281 fatcat:7fhix4ln3faijnhyqfwaocjnqq
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