On the product of Hurwitz zeta-functions

Wang, Nian Liang; Banerjee, Soumyarup

doi:10.3792/pjaa.93.31

Cited by 6 publications

(3 citation statements)

References 10 publications

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“…Wilton's approach to prove Theorem A involves techniques of real and complex analysis. Recently, D. Banerjee and J. Mehta [1] gave an alternative proof of Theorem A using number theoretic approach, and a similar result for Hurwitz zeta functions appeared in [15]. In this paper, we obtain an analogous result to that of Theorem A in number fields.…”

supporting

confidence: 54%

An analogue of Wilton's formula and values of Dedekind zeta functions

Banerjee¹,

Chakraborty²,

Hoque³

2016

Preprint

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J. R. Wilton obtained a formula for the product of two Riemann zeta functions. This formula played a crucial role to find the approximate functional equation for the product of two Riemann zeta functions in the critical region. We find an analogous formula for the product of two Dedekind zeta functions and then use this formula to find closed form expressions for Dedekind zeta values attached to arbitrary real as well as quadratic number fields at any positive integer.

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supporting

confidence: 54%

An analogue of Wilton's formula and values of Dedekind zeta functions

Banerjee¹,

Chakraborty²,

Hoque³

2016

Preprint

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“…which amounts to (61) on clearing the denominators and multiplying by (π/M) (s− 1)/2 . Wang and Banerjee [46] treat the product of Hurwitz zeta-functions which satisfy a ramified functional equation as a result of the Hurwitz formula:…”

Section: Ramified Functional Equationsmentioning

confidence: 99%

Around the Lipschitz Summation Formula

Li¹,

Li²,

Mehta

2020

Mathematical Problems in Engineering

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Boundary behavior of important functions has been an object of intensive research since the time of Riemann. Kurokawa, Kurokawa-Koyama, and Chapman studied the boundary behavior of generalized Eisenstein series which falls into this category. The underlying principle is the use of the Lipschitz summation formula. Our purpose is to show that it is a form of the functional equation for the Lipschitz–Lerch transcendent (and in the long run, it is equivalent to that for the Riemann zeta-function) and that this being indeed a boundary function of the Hurwitz–Lerch zeta-function, one can extract essential information. We also elucidate the relation between Ramanujan’s formula and automorphy of Eisenstein series.

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“…The problem of estimating the error term is known as the Piltz divisor problem, named in honor of of Adolf Piltz. An error term of Voronoï-type was previously obtained by the author and Wang [16] for the shifted Piltz divisor problem; this is the problem of counting the number of lattice points lying inside or on the hyperbola after shifting the origin to a fixed coordinate. In this article, we consider the Piltz divisor problem over number fields, which we next describe.…”

Section: Introductionmentioning

confidence: 99%