To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure email@example.com
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
A new reciprocity formula for Dirichlet L-functions associated to an arbitrary primitive Dirichlet character of prime modulus q is established. We find an identity relating the fourth moment of individual Dirichlet L-functions in the t-aspect to the cubic moment of central L-values of Hecke–Maaß newforms of level at most
and primitive central character
averaged over all primitive nonquadratic characters
modulo q. Our formula can be thought of as a reverse version of recent work of Petrow–Young. Direct corollaries involve a variant of Iwaniec’s short interval fourth moment bound and the twelfth moment bound for Dirichlet L-functions, which generalise work of Jutila and Heath-Brown, respectively. This work traverses an intersection of classical analytic number theory and automorphic forms.
This chapter turns to the question of how the judgment of taste is related to cognition and to the larger conception of judgment discussed in Chapter 2. It offers a new reading and contextualization of the argument of §21, in the Fourth Moment of the Analytic of the Beautiful, which establishes a “common sense” as a necessary condition of the universal communicability of cognition. On my reading, Kant does not provide, or seek to provide, a deduction of the judgment of taste avant la lettre. His point, instead, is to show that cognition involves its own form of reflective judgment. Cognitive judgment considered from the perspective of the third Critique – actual, situated judgment – depends on a norm beyond that of correctness: of aptness or appropriateness; of what calls for judgment. My reading is an alternative not only to the widespread “aesthetic” construal of Kant’s argument, on which it is meant to establish an aesthetic common sense, but also to the “epistemic” construal proposed by Henry Allison, on which it is meant to establish an epistemic common sense.
Email your librarian or administrator to recommend adding this to your organisation's collection.