arXiv subjects

Rupam Barman

Publications and source records attributed to Rupam Barman.

57 records · Page 4Linked to original sources

arXiv2012

Hypergeometric functions and a family of algebraic curves

Let $λ\in \mathbb{Q}\setminus \{0, 1\}$ and $l \geq 2$, and denote by $C_{l,λ}$ the nonsingular projective algebraic curve over $\mathbb{Q}$ with affine equation given by $$y^l=x(x-1)(x-λ).$$ In this paper we define $Ω(C_{l, λ})$ analogous to the real periods of elliptic curves and find a relation with ordinary hypergeometric series. We also give a relation between the number of points on $C_{l, λ}$ over a finite field and Gaussian hypergeometric series. Finally we give an alternate proof of a result of \cite{rouse}.

math.NT↗

arXiv2012

Certain values of Gaussian hypergeometric series and a family of algebraic curves

Let $λ\in \mathbb{Q}\setminus \{0, -1\}$ and $l \geq 2$. Denote by $C_{l,λ}$ the nonsingular projective algebraic curve over $\mathbb{Q}$ with affine equation given by $$y^l=(x-1)(x^2+λ).$$ In this paper we give a relation between the number of points on $C_{l, λ}$ over a finite field and Gaussian hypergeometric series. We also give an alternate proof of a result of McCarthy (2010). We find some special values of ${_{3}}F_2$ and ${_{2}}F_1$ Gaussian hypergeometric series. Finally we evaluate the value of ${_{3}}F_2(4)$ which extends a result of Ono (1998).

math.NT↗

arXiv2012

Hypergeometric functions over $\mathbb{F}_q$ and traces of Frobenius for elliptic curves

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 over $\mathbb{F}_q$ for $q \equiv 1 (\text{mod} 6)$ and $q \equiv 1 (\text{mod} 4)$.

math.NT↗