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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
Journal Article
Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2017, Volume 54, Issue 3, pp. 789 - 797
Journal Article
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
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
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
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
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
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
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
Journal Article
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
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
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)
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
Journal Article
Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2019, Volume 13, Issue 1, pp. 309 - 324
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 11
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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