Gautam Kalita

activity

20122024

F_{q}

and Gaussian hypergeometric series

2 citations · 2 across the 6 of their papers we have counts for

collaborators

8 papers

math.NT2024

On some conjectural determinants of Sun involving residues

Rituparna Chaliha, Gautam Kalita

For an odd prime $p$ and integers $d, k, m$ with gcd $(p, d) = 1$ and $2 \leq k \leq \frac{p - 1}{2}$ , we consider the determinant \begin{equation*} S_{m,k}(d,p) = \left|(α_i - α_j)^m\righ…

math.NT2020

Lauricella hypergeometric series $F_{A}^{(n)}$ over finite fields

Arjun Singh Chetry, Gautam Kalita

In this paper, we develop a finite field analogue for one of the Lauricella series, $F_{A}^{(n)}$ . Extending results of Greene, a finite field analog for the multinomial coefficient…

math.NT2020

Proof of a supercongruence conjecture of (F.3) of Swisher using the WZ-method

Arijit Jana, Gautam Kalita

For a non-negative integer $m$ , let $S (m)$ denote the sum given by $S (m) := n = 0 \sum m \frac{( - 1 ) ^{n} ( 8 n + 1 )}{n ! ^{3}} (\frac{1}{4})_{n}^{3} .$ Using the powerful WZ-method, for…

math.NT2020

Extension of a conjectural supercongruence of (G.3) of Swisher using Zeilberger's algorithm

Arijit Jana, Gautam Kalita

Using Zeilberger's algorithm, we here give a proof of the supercongruence $$ \sum_{n=0}^{\frac{p^r-3}{4}}(8n+1)\frac{\left(\frac{1}{4}\right)_n^4}{(1)_n^4}\equiv -p^3 \sum_{n=0}^{\…

math.NT2013★ 2 cited

Hyperelliptic curves over $F_{q}$ and Gaussian hypergeometric series

Rupam Barman, Gautam Kalita

Let $d \geq 2$ be an integer. Denote by $E_{d}$ and $E_{d}^{'}$ the hyperelliptic curves over $F_{q}$ given by $E_{d} : y^{2} = x^{d} + a x + b and E_{d}^{'} : y^{2} = x^{d} + a x^{d - 1} + b,$ resp…

math.NT2012

Hypergeometric functions over $F_{q}$ and traces of Frobenius for elliptic curves

Rupam Barman, Gautam Kalita

We present here explicit relations between the traces of Frobenius endomorphisms of certain families of elliptic curves and special values of $_{2} F_{1}$ -hypergeometric functions o…

On some conjectural determinants of Sun involving residues

Lauricella hypergeometric series FA(n)​ over finite fields

Proof of a supercongruence conjecture of (F.3) of Swisher using the WZ-method

Extension of a conjectural supercongruence of (G.3) of Swisher using Zeilberger's algorithm

Hyperelliptic curves over Fq​ and Gaussian hypergeometric series

Hypergeometric functions over Fq​ and traces of Frobenius for elliptic curves

Lauricella hypergeometric series $F_{A}^{(n)}$ over finite fields

Hyperelliptic curves over $F_{q}$ and Gaussian hypergeometric series

Hypergeometric functions over $F_{q}$ and traces of Frobenius for elliptic curves