The universality of zeta-functions attached to certain cusp forms
Antanas Laurinčikas, Kohji Matsumoto (2001)
Acta Arithmetica
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Antanas Laurinčikas, Kohji Matsumoto (2001)
Acta Arithmetica
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Masanori Katsurada (2001)
Acta Arithmetica
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Goro Shimura (1995)
Inventiones mathematicae
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Yoichi Motohashi (1995)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Đurđe Cvijović, Jacek Klinowski (2000)
Matematički Vesnik
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Masanori Katsurada (2003)
Acta Arithmetica
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Takumi Noda (2015)
Acta Arithmetica
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Zeta-functions associated with modified Bessel functions are introduced as ordinary Dirichlet series whose coefficients are J-Bessel and K-Bessel functions. Integral representations, transformation formulas, a power series expansion involving the Riemann zeta-function and a recurrence formula are given. The inverse Laplace transform of Weber's first exponential integral is the basic tool to derive the integral representations. As an application, we give a new proof of the Fourier series...
Wolfgang Müller (1992)
Monatshefte für Mathematik
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Stéphane R. Louboutin (2007)
Colloquium Mathematicae
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We give a simple proof of the Siegel-Tatuzawa theorem according to which the residues at s = 1 of the Dedekind zeta functions of quadratic number fields are effectively not too small, with at most one exceptional quadratic field. We then give a simple proof of the Brauer-Siegel theorem for normal number fields which gives the asymptotics for the logarithm of the product of the class number and the regulator of number fields.
Yoshitaka Sasaki (2009)
Acta Arithmetica
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Kohji Matsumoto, Takashi Nakamura, Hiroyuki Ochiai, Hirofumi Tsumura (2008)
Acta Arithmetica
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Henry H. Kim (1994)
Manuscripta mathematica
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Kazuhiro Onodera (2014)
Acta Arithmetica
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We generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give new integral representations of several zeta functions, an extension of the parity result to the whole domain of convergence, concrete expressions of Tornheim's double zeta function at non-positive integers and some results on the behavior of a certain Witten's zeta...
J. Elstrodt, F. Grunewald (1985)
Journal für die reine und angewandte Mathematik
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