Dirichlet series and gamma function associated with rational functions

• Autorzy: Spreafico M.
• Języki publikacji: EN

Abstrakty

EN

We investigate zeta regularized products of rational functions. As an application, we obtain the asymptotic expansion of the Euler Gamma function associated with a rational function.

Słowa kluczowe

EN

rational function; Riemann zeta function; zeta regularized product

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: Vol. 58, no 3
• Strony: 189--195
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Spreafico M.

• ICMC, Universidade de Sao Paulo Sao Carlos, Brazil,

Bibliografia

• [1] J. Brüning and R. Seeley, The resolvent expansion for second order regular singular operators, J. Funct. Anal. 73 (1988), 369-415.
• [2] E. T. Copson, Theory of Functions of a Complex Variable, Oxford Univ. Press, 1935.
• [3] A. Dąbrowski, On zeta functions associated with polynomials, Bull. Austral. Math. Soc. 61 (2000), 455-458.
• [4] M. Eie, On Dirichlet series associated with a polynomial, Proc. Amer. Math. Soc. 110 (1990), 583-590.
• [5] M. Eie and K.-W. Chen, A theorem on zeta functions associated with polynomials, Trans. Amer. Math. Soc. 351 (1999), 3217-3228.
• [6] M. Spreafico, Zeta invariants for sequences of spectral type, special functions and the Lerch formula, Proc. Roy. Soc. Edinburgh 281 (2006), 865-889.
• [7] M. Spreafico, Zeta invariants for double sequences of spectral type, arXiv:math/0607816.
• [8] E. T. Whittaker and G. N. Watson, Modern Analysis, Cambridge Univ. Press, 1963.