The fourth moment of Dirichlet L-functions

By M. Young. 2006

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We compute the fourth moment of Dirichlet L-functions at the central point for prime moduli, with a power savings in the error term.

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The fourth moment of Dirichlet L-functions along a coset and the Weyl bound (2019, background): “In [Y1] the second author derived a similar duality in q-aspect: ∑”
Sommes de Gál et applications (2018, background): “D’après le lemme 1 de [22] (voir aussi le lemme 3 de [11]), lorsque (mn, q) = 1, nous avons”
The quantum unique ergodicity conjecture for thin sets (2013, methodology): “= w(x− m) has support on x≍ Y too. 8.1. Separation of variables. As a starting point, we ﬁnd it convenient to appeal to an approximate functional equation for the divisor function, as in Lemma 5.4 of [Y]. This is a particularly simple alternative to the circle method or the delta symbol method for t”
On moments of twisted L-functions (2014, methodology): “We proceed by Mellin inversion (as in [3, 29]): using the definition (2.”
The second moment of quadratic twists of modular L-functions (2009, unknown): “A similar truncation argument appeared in [16].”
Bilinear forms with Kloosterman sums and applications (2015, unknown): “, the average of the fourth moment of L(χ, 1/2)) was solved by Matt Young [39] and the general case (when f or g or both might be cuspidal) was studied in [2, 3], as already mentioned.”