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Deriving two dualities simultaneously from a family of identities for multiple harmonic sums
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We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two kinds of limit operations, we obtain new proofs of both the duality for multiple zeta values and the duality for finite multiple zeta values.
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Cited by 3 Pith papers
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Positive characteristic analogues of finite algebraic numbers
A positive-characteristic analogue of Rosen's finite algebraic numbers is introduced over F_q(θ) and is characterized by linear recurrent sequences with separable eigen polynomial, Frobenius evaluation, and matrix coe...
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Truncated Hypergeometric Functions and Discretized Integrals
A new truncation of the hypergeometric series obeys an exact discretized-integral identity, and a finite analogue of the Ohno-Zagier formula is proved.
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Multiple Zeta Values
An extensive expository survey of multiple zeta values, their finite/symmetric and q-analogue variants, and their modular-form connections, proving no new theorem.
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