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In this paper we establish certain identities connecting $p$-adichypergeometric functions with 4-th twisted Kloosterman sheaf sum. To provethese identities we express certain character sum over finite field in terms ofspecial values of $p$-adic hypergeometric functions. One conjecture of Evansbehaves as a bridge to connect $p$-adic hypergeometric functions withKloosterman sheaf sum. We also connect $p$-adic hypergeometric functions withFourier coefficients of certain modular forms.

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