Abstract
We show that certain twists of Bessel type of a given L-function have meromorphic continuation over \(\mathbb{C}\).
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B.L.J. Braaksma, Asymptotic expansions and analytic continuations for a class of Barnes-integrals. Compos. Math. 15, 239–341 (1964)
J.B. Conrey, A. Ghosh, On the Selberg class of Dirichlet series: small degrees. Duke Math. J. 72, 673–693 (1993)
A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, vol. 2 (McGraw-Hill, New York, 1953)
J. Kaczorowski, Axiomatic theory of L-functions: the Selberg class, in Analytic Number Theory, C.I.M.E. Summer School, Cetraro (Italy) 2002, ed. by A. Perelli, C. Viola. Lecture Notes in Mathematics, vol. 1891 (Springer, Berlin/Heidelberg, 2006), pp. 133–209
J. Kaczorowski, A. Perelli, On the structure of the Selberg class, I: 0 ≤ d ≤ 1. Acta Math. 182, 207–241 (1999)
J. Kaczorowski, A. Perelli, The Selberg class: a survey, in Number Theory in Progress, Proc. Conf. in Honor of A.Schinzel, ed. by K. Györy et al. (de Gruyter, Berlin, 1999), pp. 953–992
J. Kaczorowski, A. Perelli, On the structure of the Selberg class, VI: non-linear twists. Acta Arithmetica 116, 315–341 (2005)
J. Kaczorowski, A. Perelli, On the structure of the Selberg class, VII: 1 < d < 2. Ann. Math. 173, 1397–1441 (2011)
J. Kaczorowski, A. Perelli, Twists and resonance of L-functions, I. To appear in J. European Math. Soc.
J. Kaczorowski, A. Perelli, Twists and resonance of L-functions, II. Preprint (2014)
M.R. Murty, Selberg’s conjectures and Artin L-functions. Bull. Am. Math. Soc. 31, 1–14 (1994)
T. Noda, On the functional properties of Bessel zeta-functions. Submittted
T. Noda, On the functional properties of the confluent hypergeometric zeta-function. To appear in Ramanujan J
A. Perelli, A survey of the Selberg class of L-functions, part II. Riv. Mat. Univ. Parma 3*(7), 83–118 (2004)
A. Perelli, A survey of the Selberg class of L-functions, part I. Milan J. Math. 73, 19–52 (2005)
A. Perelli, Non-linear twists of L-functions: a survey. Milan J. Math. 78, 117–134 (2010)
A. Selberg, Old and new conjectures and results about a class of Dirichlet series, in Proc. Amalfi Conf. Analytic Number Theory, ed. by E. Bombieri et al. (Università di Salerno, Salerno, 1992), pp. 367–385; Collected Papers, vol. 2 (Springer, Berlin, 1991), pp. 47–63
Acknowledgements
This research was partially supported by the MIUR grant PRIN2010-11 Arithmetic Algebraic Geometry and Number Theory and by grant 2013/11/B/ST1/ 02799 Analytic Methods in Arithmetic of the National Science Centre.
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Dedicated to Professor Helmut Maier for his 60th birthday
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Kaczorowski, J., Perelli, A. (2015). A Note on Bessel Twists of L-Functions. In: Pomerance, C., Rassias, M. (eds) Analytic Number Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-22240-0_13
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DOI: https://doi.org/10.1007/978-3-319-22240-0_13
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