The Experts below are selected from a list of 18684 Experts worldwide ranked by ideXlab platform
Noriyuki Otsubo - One of the best experts on this subject based on the ideXlab platform.
-
cm periods cm regulators and Hypergeometric Functions i
Canadian Journal of Mathematics, 2017Co-Authors: Masanori Asakura, Noriyuki OtsuboAbstract:We prove the Gross–Deligne conjecture on CM periods for motives associated with of certain surfaces fibered over the projective line. Then we prove for the same motives a formula which expresses the -regulators in terms of Hypergeometric Functions , and obtain a new example of non-trivial regulators.
-
cm periods cm regulators and Hypergeometric Functions i
arXiv: Number Theory, 2015Co-Authors: Masanori Asakura, Noriyuki OtsuboAbstract:We study the $H^2$ of certain surfaces with complex multiplication by a cyclotomic field. The periods are written in terms of values of the gamma function and the conjecture of Gross-Deligne is verified. The regulators of certain $K_1$-elements are written in terms of values of Hypergeometric Functions ${}_3F_2$, and we prove their non-vanishing.
Alexander Varchenko - One of the best experts on this subject based on the ideXlab platform.
-
modular transformations of the elliptic Hypergeometric Functions macdonald polynomials and the shift operator
Moscow Mathematical Journal, 2003Co-Authors: Giovanni Felder, Laura Stevens, Alexander VarchenkoAbstract:We consider the space of elliptic Hypergeometric Functions of the sl2 type associated with elliptic curves with one marked point. This space represents conformal blocks in the sl2 WZW model of CFT. The modular group acts on this space. We give formulas for the matrices of the action in terms of values at roots of unity of Macdonald polynomials of the sl2 type.
-
quantized knizhnik zamolodchikov equations quantum yang baxter equation and difference equations for q Hypergeometric Functions
Communications in Mathematical Physics, 1994Co-Authors: Alexander VarchenkoAbstract:Thesl2 quantized Knizhnik-Zamolodchikov equations are solved inq-Hypergeometric Functions. New difference equations are derived for generalq-Hypergeometric Functions. The equations are given in terms of quantum Yang-Baxter matrices and have the form similar to quantum Knizhnik-Zamolodchikov equations for quantum affine algebras introduced by Frenkel and Reshetikhin.
H M Srivastava - One of the best experts on this subject based on the ideXlab platform.
-
some extensions of the pochhammer symbol and the associated Hypergeometric Functions
Iranian Journal of Science and Technology Transaction A-science, 2019Co-Authors: H M Srivastava, Gauhar Rahman, Kottakkaran Sooppy NisarAbstract:In the present paper, we first define an extended Pochhammer symbol by using a known extension of the gamma function involving the modified Bessel (or Macdonald) function. By using this extended Pochhammer symbol, we then introduce and investigate the corresponding extension of the generalized Hypergeometric function and of some of its special cases. We also present some families of generating Functions and generating relations for the extended Hypergeometric Functions.
-
a certain generalized pochhammer symbol and its applications to Hypergeometric Functions
Applied Mathematics and Computation, 2014Co-Authors: H M Srivastava, Aysegul Cetinkaya, Onur I KiymazAbstract:In this article, we first introduce an interesting new generalization of the familiar Pochhammer symbol by means of a certain one-parameter family of generalized gamma Functions. With the help of this new generalized Pochhammer symbol, we then introduce an extension of the generalized Hypergeometric function "rF"s with r numerator and s denominator parameters. Finally, we present a systematic study of the various fundamental properties of the class of the generalized Hypergeometric Functions introduced here.
-
certain fractional integral operators and the generalized incomplete Hypergeometric Functions
2013Co-Authors: H M Srivastava, Praveen AgarwalAbstract:In this paper, we apply a certain general pair of operators of fractional integration involving Appell's function F3 in their kernel to the generalized incomplete Hypergeometric Functions pq(z) and p q(z), which were introduced and studied systematically by Srivastava et al. in the year 2012. Some interesting special cases and consequences of our main results are also considered.
-
a class of extended fractional derivative operators and associated generating relations involving Hypergeometric Functions
Axioms, 2012Co-Authors: H M Srivastava, Rakesh K Parmar, Purnima ChopraAbstract:Recently, an extended operator of fractional derivative related to a generalized Beta function was used in order to obtain some generating relations involving the extended Hypergeometric Functions [1]. The main object of this paper is to present a further generalization of the extended fractional derivative operator and apply the generalized extended fractional derivative operator to derive linear and bilinear generating relations for the generalized extended Gauss, Appell and Lauricella Hypergeometric Functions in one, two and more variables. Some other properties and relationships involving the Mellin transforms and the generalized extended fractional derivative operator are also given.
-
integral representations for srivastava s triple Hypergeometric Functions
Taiwanese Journal of Mathematics, 2011Co-Authors: Junesang Choi, H M Srivastava, Anvar Hasanov, Mamasali TuraevAbstract:While investigating the Lauricella's list of 14 complete second-order Hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple Hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple Hypergeometric Functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for each of Srivastava's triple Hypergeometric Functions $H_A$, $H_B$ and $H_C$.
Masanori Asakura - One of the best experts on this subject based on the ideXlab platform.
-
cm periods cm regulators and Hypergeometric Functions i
Canadian Journal of Mathematics, 2017Co-Authors: Masanori Asakura, Noriyuki OtsuboAbstract:We prove the Gross–Deligne conjecture on CM periods for motives associated with of certain surfaces fibered over the projective line. Then we prove for the same motives a formula which expresses the -regulators in terms of Hypergeometric Functions , and obtain a new example of non-trivial regulators.
-
cm periods cm regulators and Hypergeometric Functions i
arXiv: Number Theory, 2015Co-Authors: Masanori Asakura, Noriyuki OtsuboAbstract:We study the $H^2$ of certain surfaces with complex multiplication by a cyclotomic field. The periods are written in terms of values of the gamma function and the conjecture of Gross-Deligne is verified. The regulators of certain $K_1$-elements are written in terms of values of Hypergeometric Functions ${}_3F_2$, and we prove their non-vanishing.
Matti Vuorinen - One of the best experts on this subject based on the ideXlab platform.
-
LANDEN INEQUALITIES FOR ZERO-BALANCED Hypergeometric Functions
2016Co-Authors: Slavko Simic, Matti VuorinenAbstract:Abstract. For zero-balanced Gaussian Hypergeometric Functions F (a, b; a+b;x), a, b> 0, we determine maximal regions of ab plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each x ∈ (0, 1). Thereby an exhausting answer is given to the open problem from [AVV]
-
landen inequalities for zero balanced Hypergeometric Functions
Abstract and Applied Analysis, 2012Co-Authors: Slavko Simic, Matti VuorinenAbstract:For zero-balanced Gaussian Hypergeometric Functions , , we determine maximal regions of plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each . Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990.
-
landen inequalities for zero balanced Hypergeometric Functions
arXiv: Classical Analysis and ODEs, 2011Co-Authors: Slavko Simic, Matti VuorinenAbstract:For zero-balanced Gaussian Hypergeometric Functions $ F(a,b;a+b;x),$ $a,b>0,$ we determine maximal regions of $ab$ plane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for each $x\in (0,1)$. Thereby an exhausting answer is given to an open problem.
-
on Hypergeometric Functions and function spaces
Journal of Computational and Applied Mathematics, 2002Co-Authors: R Balasubramanian, Saminathan Ponnusamy, Matti VuorinenAbstract:The aim of this paper is to discuss the role of Hypergeometric Functions in function spaces and to prove some new results for these Functions. The first part of this paper proves results such as monotone, convexity and concavity properties of sums of products of Hypergeometric Functions. The second part of our results deals with the space A of all normalized analytic Functions f, f(0) = 0 = f'(0) - 1, in the unit disk Δ and the subspace R(β) = {f ∈ A: A n ∈ R such that Re eiη (f'(z) - β)>0, z ∈ Δ}. For f ∈ A, we consider integral transforms of the type Vλ(f) = ∫01 λ(t) f(tz)/t dt, where λ(t) is a real valued nonnegative weight function normalized so that ∫01 λ(t)= 1. We obtain conditions on β and the function λ such that Vλ(f) takes each member of R(β) into a starlike function of order β, β ∈ [0,1/2]. These results extend and improve the earlier known results in these directions. We end the paper with an open problem.