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Background We have recently found that exposure to acute restraint stress suppresses antigen-specific antibody production, including IgE, in a murine model of allergic rhinitis. Although age-related alterations in immune responses are known, it remains unclear whether aging modulates the antibody production under stressful conditions. In this study, we set out to determine the effects of aging on antibody production under acute restraint stress in mice. Methods Both young and aged CBA/J mice were repeatedly sensitized intranasally with phospholipase A2 (PLA2) without adjuvants. Restraint stress was applied using uniform cylinders once a week for a continuous 8 h period, on 5 occasions in total. Blood samples were taken at 0, 20 and 30 days after primary sensitization, and production of PLA2-specific antibodies and levels of IL-4, IFN-γ, IL-10 and IL-1β in sera were determined by ELISA. Results Repeated intranasal sensitization with PLA2 induced PLA2-specific IgE, IgG1 and IgG2a production in aged mice. We found that exposure to restraint stress significantly inhibited production of PLA2-specific IgE, IgG1 and IgG2a in aged mice. In addition, antibody production under restraint stress decreased significantly in aged mice when compared with young mice. No IL-4, IFN-γ, IL-10 or IL-1β were detected in sera from non-stressed or stressed aged mice. Conclusions Aging exacerbates the immunosuppressive role of acute restraint stress in antigen-specific antibody production in mice.

We consider an effective lower bound of the Siegel-Tatuzawa type for general L-functions with three standard assumptions. We further assume three hypotheses in this paper that are essential in developing our argument.Under these assumptions and hypotheses, we prove a theorem of Siegel-Tatuzawa type for general L-functions. In particular, we prove such a theorem for symmetric power L-functions under certain assumptions.

Rankin obtained the asymptotic formula for the sum of coefficients of Rankin-Selberg $L$ -series associated with a cusp form and a trivial character. $\mathrm{Ivi}\acute{\mathrm{c}}-$ Matsumoto-Tanigawa studied the error term in it by using a mean value formula which is yielded from the Voronoï formula of the Riesz mean. In this paper, we consider more general Rankin-Selberg $L$ -series. It is associated with two cusp forms and a nontrivial character mod $d$ . $\mathrm{Ivi}\acute{\mathrm{c}}$ -Matsumoto-Tanigawa's method cannot be applied directly to our case. We consider the sum of coefficients of twisted Rankin-Selberg $L$ -series by a modification of their method.