N. Saikia

activity

20132023

most citedCounting Points on Dwork Hypersurfaces and

p

-adic Gamma Function

6 citations · 11 across the 11 of their papers we have counts for

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14 papers · 1 filter

math.NT2023

Values of $p$ -adic hypergeometric functions, and $p$ -adic analogue of Kummer's linear identity

Neelam Saikia

Let $p$ be an odd prime and $F_{p}$ be the finite field with $p$ elements. This paper focuses on the study of values of a generic family of hypergeometric functions in the $…

math.NT2022

Sato-Tate Distribution of $p$ -adic hypergeometric functions

Sudhir Pujahari, Neelam Saikia

Recently Ono, Saad and the second author \cite{KHN} initiated a study of value distribution of certain families of Gaussian hypergeometric functions over large finite fields. They…

math.NT2021

AGM and jellyfish swarms of elliptic curves

Michael J. Griffin, Ken Ono, Neelam Saikia +1

The classical $AGM$ produces wonderful interdependent infinite sequences of arithmetic and geometric means with common limit. For finite fields $F_{q},$ with $q\equ…

math.NT2021★ 3 cited

Distribution of values of Gaussian hypergeometric functions

Ken Ono, Hasan Saad, Neelam Saikia

In the 1980's, Greene defined {\it hypergeometric functions over finite fields} using Jacobi sums. The framework of his theory establishes that these functions possess many propert…

math.NT2020

Zeros of hypergeometric functions in the $p$ -adic setting

Neelam Saikia

Let $p$ be an odd prime and $F_{p}$ be the finite field with $p$ elements. McCarthy \cite{mccarthy-pacific} initiated a study of hypergeometric functions in the $p$ -adic set…

math.NT2020

$p$ -Adic hypergeometric functions in the connections with certain twisted Kloosterman sheaf sum and modular forms

Neelam Saikia

In this paper we establish certain identities connecting $p$ -adic hypergeometric functions with 4-th twisted Kloosterman sheaf sum. To prove these identities we express certain cha…

math.NT2020

Zeros of $p$ -adic hypergeometric functions, $p$ -adic analogues of Kummer's and Pfaff's identities

Neelam Saikia

We classify all the zeros and non-zero values of a family of hypergeometric series in the $p$ -adic setting. These values of hypergeometric series in the $p$ -adic setting lead to tr…

math.NT2018

Certain character sums and hypergeometric series

Rupam Barman, Neelam Saikia

We prove two transformations for the $p$ -adic hypergeometric series which can be described as $p$ -adic analogues of a Kummer's linear transformation and a transformation of Clausen…

math.NT2016

Summation identities and transformations for hypergeometric series

Rupam Barman, Neelam Saikia

We find summation identities and transformations for the McCarthy's $p$ -adic hypergeometric series by evaluating certain Gauss sums which appear while counting points on the family…

math.NT2015★ 6 cited

Counting Points on Dwork Hypersurfaces and $p$ -adic Gamma Function

Rupam Barman, Hasanur Rahman, Neelam Saikia

We express the number of points on the Dwork hypersurface $X_{λ}^{d} : x_{1}^{d} + x_{2}^{d} + \dots + x_{d}^{d} = d λ x_{1} x_{2} \dots x_{d}$ over a finite field of order $q \neq \equiv 1 (mod d)$ in terms o…

math.NT2015★ 2 cited

Supercongruences for truncated hypergeometric series and p-adic gamma function

Rupam Barman, Neelam Saikia

We prove three more general supercongruences between truncated hypergeometric series and $p$ -adic Gamma function from which some known supercongruences follow. A supercongruence co…

math.NT2014

Summation identities and special values of hypergeometric series in the $p$ -adic setting

Rupam Barman, Neelam Saikia, Dermot McCarthy

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 families of hyperellipti…

math.NT2014

Certain Transformations for Hypergeometric series in $p$ -adic setting

Rupam Barman, Neelam Saikia

In \cite{mccarthy2}, McCarthy defined a function $_{n} G_{n} [\dots]$ using the Teichmüller character of finite fields and quotients of the $p$ -adic gamma function. This function ex…

math.NT2013

p-adic Gamma function and traces of Frobenius of elliptic curves

Rupam Barman, Neelam Saikia

In \cite{mccarthy2}, McCarthy defined a function $_{n} G_{n} [\dots]$ using Teichmüller character of finite fields and quotients of $p$ -adic gamma function, and expressed the trace…

Values of p-adic hypergeometric functions, and p-adic analogue of Kummer's linear identity

Sato-Tate Distribution of p-adic hypergeometric functions

AGM and jellyfish swarms of elliptic curves

Distribution of values of Gaussian hypergeometric functions

Zeros of hypergeometric functions in the p-adic setting

p-Adic hypergeometric functions in the connections with certain twisted Kloosterman sheaf sum and modular forms

Zeros of p-adic hypergeometric functions, p-adic analogues of Kummer's and Pfaff's identities

Certain character sums and hypergeometric series

Summation identities and transformations for hypergeometric series

Counting Points on Dwork Hypersurfaces and p-adic Gamma Function

Supercongruences for truncated hypergeometric series and p-adic gamma function

Summation identities and special values of hypergeometric series in the p-adic setting

Certain Transformations for Hypergeometric series in p-adic setting

p-adic Gamma function and traces of Frobenius of elliptic curves

Values of $p$ -adic hypergeometric functions, and $p$ -adic analogue of Kummer's linear identity

Sato-Tate Distribution of $p$ -adic hypergeometric functions

Zeros of hypergeometric functions in the $p$ -adic setting

$p$ -Adic hypergeometric functions in the connections with certain twisted Kloosterman sheaf sum and modular forms

Zeros of $p$ -adic hypergeometric functions, $p$ -adic analogues of Kummer's and Pfaff's identities

Counting Points on Dwork Hypersurfaces and $p$ -adic Gamma Function

Summation identities and special values of hypergeometric series in the $p$ -adic setting

Certain Transformations for Hypergeometric series in $p$ -adic setting