1990, Encyclopedia of mathematics and its applications, ISBN 9780521350495, Volume 35, xx, 287

Book

1985, Ellis Horwood series in mathematics and its applications. Statistics and operational research., ISBN 9780853126027, 425

Book

1998, Memoirs of the American Mathematical Society, ISBN 0821808117, Volume no. 642., viii, 99

Book

Annales mathématiques du Québec, ISSN 2195-4755, 10/2018, Volume 42, Issue 2, pp. 133 - 157

We find summation identities and transformations for the McCarthy’s p-adic hypergeometric series by evaluating certain Gauss sums which appear while counting...

11S80 | Teichmüller character | Secondary 33C99 | 33E50 | Gaussian hypergeometric series | Mathematics | p -adic Gamma function | Primary 11G20 | Jacobi sums | Algebra | Gauss sums | Analysis | Character of finite fields | p -adic hypergeometric series | Mathematics, general | Algebraic curves | Number Theory | 11T24 | p-adic Gamma function | p-adic hypergeometric series

11S80 | Teichmüller character | Secondary 33C99 | 33E50 | Gaussian hypergeometric series | Mathematics | p -adic Gamma function | Primary 11G20 | Jacobi sums | Algebra | Gauss sums | Analysis | Character of finite fields | p -adic hypergeometric series | Mathematics, general | Algebraic curves | Number Theory | 11T24 | p-adic Gamma function | p-adic hypergeometric series

Journal Article

Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2017, Volume 54, Issue 3, pp. 789 - 797

The main purpose of this paper is to present closed integral form expressions for the Mathieu-type a-series and its associated alternating version whose terms...

Cahen formula | (p,q)-extended Gaussian hyper-geometric function | Integral representations | Bounding inequality | Mathieu–type series | (p,q)-extended Beta function | (p, q)-extended Beta function | MATHEMATICS | Mathieu-type series | bounding inequality | (p, q)-extended Gaussian hypergeometric function | integral representations | INTEGRAL-REPRESENTATION | TERMS CONTAIN

Cahen formula | (p,q)-extended Gaussian hyper-geometric function | Integral representations | Bounding inequality | Mathieu–type series | (p,q)-extended Beta function | (p, q)-extended Beta function | MATHEMATICS | Mathieu-type series | bounding inequality | (p, q)-extended Gaussian hypergeometric function | integral representations | INTEGRAL-REPRESENTATION | TERMS CONTAIN

Journal Article

1988, ISBN 9780821815243, xiii, 124

Book

Journal de Théorie des Nombres de Bordeaux, ISSN 1246-7405, 1/2016, Volume 28, Issue 1, pp. 115 - 124

Let be an elliptic curve described by either an Edwards model or a twisted Edwards model over 𝔽 , namely, is defined by one of the following equations ² + ² =...

Series convergence | Algebra | Finite fields | Edwards curves | Gaussian hypergeometric series | MATHEMATICS | Finite Fields | Gaussian Hypergeometric Series | Edwards Curves

Series convergence | Algebra | Finite fields | Edwards curves | Gaussian hypergeometric series | MATHEMATICS | Finite Fields | Gaussian Hypergeometric Series | Edwards Curves

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 11/2012, Volume 8, Issue 7, pp. 1581 - 1612

We define a function which extends Gaussian hypergeometric series to the p-adic setting. This new function allows results involving Gaussian hypergeometric...

generalized hypergeometric series | supercongruence | p-adic gamma function | hypergeometric functions over finite fields | Gaussian hypergeometric series | MATHEMATICS | CONGRUENCE | SUPERCONGRUENCE CONJECTURE | Electronic components industry | Mathematics - Number Theory

generalized hypergeometric series | supercongruence | p-adic gamma function | hypergeometric functions over finite fields | Gaussian hypergeometric series | MATHEMATICS | CONGRUENCE | SUPERCONGRUENCE CONJECTURE | Electronic components industry | Mathematics - Number Theory

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 2/2019, Volume 48, Issue 2, pp. 357 - 368

A Huff curve over a field K is an elliptic curve defined by the equation $$ax(y^2-1)=by(x^2-1)$$ a x ( y 2 - 1 ) = b y ( x 2 - 1 ) where $$a,b\in K$$ a , b ∈ K...

Gaussian hypergeometric functions | Functions of a Complex Variable | Field Theory and Polynomials | 14H52 | Mathematics | Huff curves | 11D45 | 11G20 | Fourier Analysis | Elliptic curves | Rational points | Number Theory | Combinatorics | 11T24

Gaussian hypergeometric functions | Functions of a Complex Variable | Field Theory and Polynomials | 14H52 | Mathematics | Huff curves | 11D45 | 11G20 | Fourier Analysis | Elliptic curves | Rational points | Number Theory | Combinatorics | 11T24

Journal Article

RAMANUJAN JOURNAL, ISSN 1382-4090, 02/2019, Volume 48, Issue 2, pp. 357 - 368

A Huff curve over a field K is an elliptic curve defined by the equation ax(y(2)-1) = by(x(2)-1) where a,b is an element of K are such that a(2) not equal...

HYPERELLIPTIC CURVES | MATHEMATICS | Elliptic curves | Gaussian hypergeometric functions | Rational points | VALUES | Huff curves | FAMILY

HYPERELLIPTIC CURVES | MATHEMATICS | Elliptic curves | Gaussian hypergeometric functions | Rational points | VALUES | Huff curves | FAMILY

Journal Article

Journal of Number Theory, ISSN 0022-314X, 09/2013, Volume 133, Issue 9, pp. 3099 - 3111

We express the trace of Frobenius of certain families of elliptic curves in terms of Gaussian hypergeometric functions. We also find some special values of F12...

Trace of Frobenius endomorphism | Elliptic curves | Gaussian hypergeometric functions | MATHEMATICS

Trace of Frobenius endomorphism | Elliptic curves | Gaussian hypergeometric functions | MATHEMATICS

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 02/2018, Volume 14, Issue 1, pp. 1 - 18

In this paper, we explicitly evaluate certain special values of 2 F 1 hypergeometric series. These evaluations are based on some summation transformation...

Algebraic curves | traces of Frobenius endomorphism | elliptic curves | Gaussian hypergeometric series | MATHEMATICS | ELLIPTIC-CURVES | RODRIGUEZ-VILLEGAS | FINITE-FIELDS | SUPERCONGRUENCE CONJECTURE | CONGRUENCES

Algebraic curves | traces of Frobenius endomorphism | elliptic curves | Gaussian hypergeometric series | MATHEMATICS | ELLIPTIC-CURVES | RODRIGUEZ-VILLEGAS | FINITE-FIELDS | SUPERCONGRUENCE CONJECTURE | CONGRUENCES

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 4/2014, Volume 102, Issue 4, pp. 345 - 355

We express the number of $${\mathbb{F}_q}$$ F q -points on the hyperelliptic curve $${\alpha{y}^2=\beta{x}^f + \gamma}$$ α y 2 = β x f + γ in terms of Gaussian...

Hyperelliptic curves | Elliptic curves | Trace of Frobenius | 33C20 | Gaussian hypergeometric series | Mathematics, general | Mathematics | 11G20 | MATHEMATICS | ELLIPTIC-CURVES | FINITE-FIELDS | ALGEBRAIC-CURVES

Hyperelliptic curves | Elliptic curves | Trace of Frobenius | 33C20 | Gaussian hypergeometric series | Mathematics, general | Mathematics | 11G20 | MATHEMATICS | ELLIPTIC-CURVES | FINITE-FIELDS | ALGEBRAIC-CURVES

Journal Article

14.
Full Text
Summation identities and special values of hypergeometric series in the p-adic setting

Journal of Number Theory, ISSN 0022-314X, 08/2015, Volume 153, pp. 63 - 84

We prove hypergeometric type summation identities for a function defined in terms of quotients of the p-adic gamma function by counting points on certain...

Character of finite fields | Hyperelliptic curves | Teichmüller character | p-Adic gamma function | Gaussian hypergeometric series | P-Adic gamma function | Secondary | Primary | Teichmuller character | TRACE | MATHEMATICS | ELLIPTIC-CURVES | FINITE-FIELDS | GAMMA-FUNCTION | FROBENIUS

Character of finite fields | Hyperelliptic curves | Teichmüller character | p-Adic gamma function | Gaussian hypergeometric series | P-Adic gamma function | Secondary | Primary | Teichmuller character | TRACE | MATHEMATICS | ELLIPTIC-CURVES | FINITE-FIELDS | GAMMA-FUNCTION | FROBENIUS

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 03/2015, Volume 11, Issue 2, pp. 645 - 660

In [The trace of Frobenius of elliptic curves and the p-adic gamma function, Pacific J. Math. 261(1) (2013) 219–236], McCarthy defined a function nGn[⋯] using...

trace of Frobenius | Character of finite fields | Teichmüller character | elliptic curves | Gaussian hypergeometric series | p-adic Gamma function | Teichmuller character | TRACE | MATHEMATICS | ELLIPTIC-CURVES | GAMMA-FUNCTION | FROBENIUS

trace of Frobenius | Character of finite fields | Teichmüller character | elliptic curves | Gaussian hypergeometric series | p-adic Gamma function | Teichmuller character | TRACE | MATHEMATICS | ELLIPTIC-CURVES | GAMMA-FUNCTION | FROBENIUS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 03/2016, Volume 276, pp. 44 - 60

In this paper, we present several generalizations and refinements for the asymptotic formulas of Gaussian and generalized hypergeometric functions.

Gaussian hypergeometric function | Generalized hypergeometric function | Asymptotical formula | Monotonicity | Inequality | MATHEMATICS, APPLIED | INEQUALITIES | SERIES | Hypergeometric functions | Mathematical models | Gaussian | Computation | Asymptotic properties | Formulas (mathematics)

Gaussian hypergeometric function | Generalized hypergeometric function | Asymptotical formula | Monotonicity | Inequality | MATHEMATICS, APPLIED | INEQUALITIES | SERIES | Hypergeometric functions | Mathematical models | Gaussian | Computation | Asymptotic properties | Formulas (mathematics)

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 12/2016, Volume 12, Issue 8, pp. 2173 - 2187

We study the character sums ϕ ( m , n ) ( a , b ) = ∑ x ∈ q ϕ ( x ( x m + a ) ( x n + b ) ) and ψ ( m , n ) ( a , b ) = ∑ x ∈ q ϕ ( ( x m + a ) ( x n + b ) ) ,...

hyperelliptic curves | Character sums | Gaussian hypergeometric series | JACOBI | MATHEMATICS | ELLIPTIC-CURVES | VALUES | JACOBSTHAL

hyperelliptic curves | Character sums | Gaussian hypergeometric series | JACOBI | MATHEMATICS | ELLIPTIC-CURVES | VALUES | JACOBSTHAL

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2019, Volume 13, Issue 1, pp. 309 - 324

Our aim in this paper, is to establish certain new integral representations for the ( )–Mathieu–type power series. In particular, we investigate the...

Mathematical series | Hypergeometric functions | Series convergence | Mathematical theorems | Mathematical integrals | Infinite series | Mathematical inequalities | Mathematical functions | Mathematics | Power series | (p, q)-extended Beta function | MATHEMATICS | MATHEMATICS, APPLIED | (p, q)-Mathieu-type series | (p, q)-Mittag-Leffler functions | (p, q)-extended Gaussian hypergeometric function | integral representations | Mellin-Barnes types integrals

Mathematical series | Hypergeometric functions | Series convergence | Mathematical theorems | Mathematical integrals | Infinite series | Mathematical inequalities | Mathematical functions | Mathematics | Power series | (p, q)-extended Beta function | MATHEMATICS | MATHEMATICS, APPLIED | (p, q)-Mathieu-type series | (p, q)-Mittag-Leffler functions | (p, q)-extended Gaussian hypergeometric function | integral representations | Mellin-Barnes types integrals

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 11

The purpose of the present paper is to investigate various mapping and inclusion properties involving subclasses of analytic and univalent functions for a...

uniformly starlike | convex function | Mathematics | hypergeometric function | univalent function | starlike function | uniformly convex | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | Hypergeometric function | Convex function | Univalent function | Starlike function | Uniformly convex | Uniformly starlike | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | STARLIKE | Usage | Convex functions | Difference equations | Gaussian processes

uniformly starlike | convex function | Mathematics | hypergeometric function | univalent function | starlike function | uniformly convex | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | Hypergeometric function | Convex function | Univalent function | Starlike function | Uniformly convex | Uniformly starlike | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | STARLIKE | Usage | Convex functions | Difference equations | Gaussian processes

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 05/2010, Volume 6, Issue 3, pp. 461 - 470

Journal Article

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