Infinite type power series subspaces of infinite type power series spaces

AbstractIn this paper several integral representations for the generalized fractional order Mathieu type power series $S_\mu (r;x) = \sum\limits_{n = 1}^\infty {\frac{{2nx^n }} {{(n^2 + r^2 )^{\mu + 1} }}(r \in \mathbb{R},\mu > 0,|x| \leqslant 1)} $ are presented. Also new integral expressions are derived for the Butzer-Flocke-Hauss (BFH) complete Omega function.

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Power series expansions of modular forms and p-adic interpolation of the square roots of Rankin–Selberg special values

International Journal of Number Theory ◽

10.1142/s1793042122500300 ◽

2021 ◽

pp. 1-41

Author(s):

Andrea Mori

Keyword(s):

Power Series ◽

Modular Forms ◽

Level Structure ◽

Automorphic Representation ◽

Base Change ◽

Series Expansions ◽

Square Roots ◽

Infinite Type ◽

Special Values ◽

Power Series Expansions

Let [Formula: see text] be a newform of even weight [Formula: see text] for [Formula: see text], where [Formula: see text] is a possibly split indefinite quaternion algebra over [Formula: see text]. Let [Formula: see text] be a quadratic imaginary field splitting [Formula: see text] and [Formula: see text] an odd prime split in [Formula: see text]. We extend our theory of [Formula: see text]-adic measures attached to the power series expansions of [Formula: see text] around the Galois orbit of the CM point corresponding to an embedding [Formula: see text] to forms with any nebentypus and to [Formula: see text] dividing the level of [Formula: see text]. For the latter we restrict our considerations to CM points corresponding to test objects endowed with an arithmetic [Formula: see text]-level structure. Also, we restrict these [Formula: see text]-adic measures to [Formula: see text] and compute the corresponding Euler factor in the formula for the [Formula: see text]-adic interpolation of the “square roots”of the Rankin–Selberg special values [Formula: see text], where [Formula: see text] is the base change to [Formula: see text] of the automorphic representation of [Formula: see text] associated, up to Jacquet-Langland correspondence, to [Formula: see text] and [Formula: see text] is a compatible family of grössencharacters of [Formula: see text] with infinite type [Formula: see text].

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Some families of generalized Mathieu-type power series, associated probability distributions and related inequalities involving complete monotonicity and log-convexity

Mathematical Inequalities & Applications ◽

10.7153/mia-2017-20-61 ◽

2017 ◽

pp. 973-986 ◽

Cited By ~ 1

Author(s):

Živorad Tomovski ◽

Khaled Mehrez

Keyword(s):

Power Series ◽

Probability Distributions ◽

Complete Monotonicity ◽

Type Power

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The Abel-type transformations intoℓ

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171299227755 ◽

1999 ◽

Vol 22 (4) ◽

pp. 775-784

Author(s):

Mulatu Lemma

Keyword(s):

Power Series ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Sequence Variant ◽

Series Method ◽

Power Series Method ◽

The Matrix ◽

Necessary And Sufficient ◽

Type Power

Lettbe a sequence in(0,1)that converges to1, and define the Abel-type matrixAα,tbyank=(k+α k)tnk+1(1−tn)α+1forα>−1. The matrixAα,tdetermines a sequence-to-sequence variant of the Abel-type power series method of summability introduced by Borwein in [1]. The purpose of this paper is to study these matrices as mappings intoℓ. Necessary and sufficient conditions forAα,tto beℓ-ℓ,G-ℓ, andGw-ℓare established. Also, the strength ofAα,tin theℓ-ℓsetting is investigated.

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Power Series Rings Over Prüfer v-multiplication Domains. II

Canadian Mathematical Bulletin ◽

10.4153/cmb-2016-046-5 ◽

2017 ◽

Vol 60 (1) ◽

pp. 63-76

Author(s):

Gyu Whan Chang

Keyword(s):

Power Series ◽

Prime Ideals ◽

Power Series Ring ◽

Series Ring ◽

Krull Domain ◽

Valuation Domains ◽

Power Series Rings ◽

Complete Integral Closure ◽

Minimal Prime ◽

Type Power

AbstractLet D be an integral domain, X1(D) be the set of height-one prime ideals of D, {Xβ} and {Xα} be two disjoint nonempty sets of indeterminates over D, D[{Xβ}] be the polynomial ring over D, and D[{Xβ}][[{Xα}]]1 be the first type power series ring over D[{Xβ}]. Assume that D is a Prüfer v-multiplication domain (PvMD) in which each proper integral t-ideal has only finitely many minimal prime ideals (e.g., t-SFT PvMDs, valuation domains, rings of Krull type). Among other things, we show that if X1(D) = Ø or DP is a DVR for all P ∊ X1(D), then D[{Xβ}][[{Xα}]]1D−{0} is a Krull domain. We also prove that if D is a t-SFT PvMD, then the complete integral closure of D is a Krull domain and ht(M[{Xβ}][[{Xα}]]1) = 1 for every height-one maximal t-ideal M of D.

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