Abstract
We prove by an elementary method the Riemann hypothesis for the local Euler factor of the zeta function of quadratic orders.
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References
M. Kaneko: A generalization of the Chowla-Selberg formula and the zeta functions of quadratic orders, Proc. Japan Acad., 66(A)-7 (1990), 201–203.
H. Weber: Lehrbuch der Algebra, Vol. 1, Chelsea, New York.
D. Zagier: Modular forms whose Fourier coefficients involve zeta functions of quadratic fields, in Modular functions of one variable VI, Lect. Notes in Math., no. 627, Springer-Verlag, (1977) 105–169.
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Kaneko, M. (2005). On the Local Factor of the Zeta Function of Quadratic Orders. In: Aoki, T., Kanemitsu, S., Nakahara, M., Ohno, Y. (eds) Zeta Functions, Topology and Quantum Physics. Developments in Mathematics, vol 14. Springer, Boston, MA. https://doi.org/10.1007/0-387-24981-8_5
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DOI: https://doi.org/10.1007/0-387-24981-8_5
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