Abstract:
Functionals of Maass and Shintani play a fundamental role in the study of classical problems of analytic number theory:
the Linnik problem on the distribution of integer points on hyperboloids and the problem of the mean value of the function of the number of divisors of quadratic
polynomials.
In the paper it is proved that these functionals on spaces
consisting of odd functions (odd with respect to the reflection operator, and for holomorphic forms of weight, which is not divisible by $ 4 $)
are zero.
Keywords:automorphic forms, Maass and Shintani functionals, spectral theory of automorphic functions.
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