On regularly varying moments for power series distributions

Slavko Simic

doi:10.2298/pim0694253s

On regularly varying moments for power series distributions

Publications de l Institut Mathematique ◽

10.2298/pim0694253s ◽

2006 ◽

Vol 80 (94) ◽

pp. 253-258 ◽

Cited By ~ 1

Author(s):

Slavko Simic

Keyword(s):

Asymptotic Behavior ◽

Entire Function ◽

Power Series ◽

Finite Order ◽

Slowly Varying Function ◽

Power Series Distribution ◽

Regularly Varying ◽

Power Series Distributions

For the power series distribution, generated by an entire function of finite order, we obtain the asymptotic behavior of its regularly varying moments. Namely, we prove that EwX??(X)\sim(EwX)??(EwX), ? > 0 (w??), where ?(?) is an arbitrary slowly varying function.

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On regularly varying moments for discrete laws

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.2009.1118 ◽

2010 ◽

Vol 47 (1) ◽

pp. 118-126

Author(s):

Slavko Simic

Keyword(s):

Entire Function ◽

Power Series ◽

Finite Order ◽

Asymptotic Relation ◽

Slowly Varying Function ◽

Regularly Varying ◽

Power Series Distributions

For a discrete law F and large n , we investigate the asymptotic relation \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$EX_n^\mu \ell (X_n ) \sim C_\mu (EX_n )^\mu \in (a,b),C_\mu > 0(EX_n \to \infty ),$$ \end{document}, where ℓ(·) is an arbitrary slowly varying function. By a result from [6], it follows that regularly varying moments for Power Series Distributions, generated by an entire function of finite order, satisfy the above relation with Cµ = 1 for each µ ∈ (0, ∞).

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On the Pólya conjecture concerning the maximum and minimum of the modulus of an entire function of finite order given by a lacunary power series

Analysis Mathematica ◽

10.1007/bf01907542 ◽

1990 ◽

Vol 16 (2) ◽

pp. 143-157 ◽

Cited By ~ 4

Author(s):

O. B. Skaskiv

Keyword(s):

Entire Function ◽

Power Series ◽

Finite Order

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Mocking the u-plane integral

Research in the Mathematical Sciences ◽

10.1007/s40687-021-00280-5 ◽

2021 ◽

Vol 8 (3) ◽

Author(s):

Georgios Korpas ◽

Jan Manschot ◽

Gregory W. Moore ◽

Iurii Nidaiev

Keyword(s):

Asymptotic Behavior ◽

Gauge Theory ◽

Entire Function ◽

Gauge Group ◽

Strong Coupling ◽

Modular Forms ◽

Correlation Functions ◽

Coulomb Branch ◽

Mock Modular Forms ◽

Donaldson Invariants

AbstractThe u-plane integral is the contribution of the Coulomb branch to correlation functions of $${\mathcal {N}}=2$$ N = 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group $$\mathrm{SU}(2)$$ SU ( 2 ) , for an arbitrary four-manifold with $$(b_1,b_2^+)=(0,1)$$ ( b 1 , b 2 + ) = ( 0 , 1 ) . The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

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Testing parameter of the power series distribution of a zero inflated power series model

Statistical Methodology ◽

10.1016/j.stamet.2006.12.001 ◽

2007 ◽

Vol 4 (4) ◽

pp. 393-406 ◽

Cited By ~ 13

Author(s):

M.K. Patil ◽

D.T. Shirke

Keyword(s):

Power Series ◽

Power Series Distribution ◽

Testing Parameter

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A NOTE ON LACUNARY POWER SERIES WITH RATIONAL COEFFICIENTS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972715001239 ◽

2015 ◽

Vol 93 (3) ◽

pp. 372-374 ◽

Cited By ~ 1

Author(s):

DIEGO MARQUES ◽

JOSIMAR RAMIREZ ◽

ELAINE SILVA

Keyword(s):

Entire Function ◽

Power Series

In this note, we prove that for any ${\it\nu}>0$, there is no lacunary entire function $f(z)\in \mathbb{Q}[[z]]$ such that $f(\mathbb{Q})\subseteq \mathbb{Q}$ and $\text{den}f(p/q)\ll q^{{\it\nu}}$, for all sufficiently large $q$.

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