Zyoiti SUETUNA’s research while affiliated with The University of Tokyo and other places

... Lavrik's method also does not depend on periodicity of the coefficients, as did various precursors in the genre of approximate functional equations for Dirichlet L-functions (most notably Riemann's formula for ζ(1/2 +it) as presented by Siegel (1932), and also Suetuna's generalization [29] (to Dirichlet L-functions) of the version of Hardy and Littlewood [11,Lemma 14]). On the other hand, the notion of an approximate functional equation for L-functions of modular forms was certainly recognized prior to Lavrik, apparent already in Hecke's original work (cf. the Fricke involution), and derived more broadly by Apostol and Sklar [1]. ...

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Comments on Deuring's zero-spacing phenomenon

... Of considerable interest is the particular case when K is the Gaussian field R(i), for in that case Δ k {x) is the error term in the classical problem of the number of lattice points in a circle. Using some results of class field theory, Suetuna [4] has obtained an improvement of Landau's result in the case when the field is normal and has abelian Galois group and k Ξ> 4. For, when the field is abelian* the theorems of Weber-Takagi tell us that ζ(s, K) is the product of k Dirichlet L-functions belonging to primitive characters. Applying his approximate functional equation for the Dirichlet L-f unctions, and using refined estimates for these in the critical strip, Suetuna then obtains the desired result. ...

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A mean value theorem for quadratic fields

... where c j > 0 and c k+1 ≥ c j . With suitable conditions on the zetafunctions, an asymptotic formula for the summatory funcions of the coeffisintes can be obtained from either from 1. On [Su3,p. 256]) the special case is stated of the Gaussian field as the problem of the number of ideals whose norm are integers [Su1] and the leading coefficient is determined. ...

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CONVOLUTION FORMULA AS A STIELTJES RESULTANT