Hybrid subconvexity for class group L-functions and uniform sup norm bounds of Eisenstein series
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Hybrid subconvexity for class group L-functions and uniform sup norm bounds of Eisenstein series. / Nordentoft, Asbjørn Christian.
In: Forum Mathematicum, Vol. 33, No. 1, 2021, p. 39-57.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Hybrid subconvexity for class group L-functions and uniform sup norm bounds of Eisenstein series
AU - Nordentoft, Asbjørn Christian
PY - 2021
Y1 - 2021
N2 - In this paper, we study hybrid subconvexity bounds for class group L-functions associated to quadratic extensions K/ℚ (real or imaginary). Our proof relies on relating the class group L-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke. The main technical contribution is the uniform sup norm bound for Eisenstein series E(z, 1/2 + it) ≪ε y1/2(|t| + 1)1/3+ε, y ≫ 1, extending work of Blomer and Titchmarsh. Finally, we propose a uniform version of the sup norm conjecture for Eisenstein series.
AB - In this paper, we study hybrid subconvexity bounds for class group L-functions associated to quadratic extensions K/ℚ (real or imaginary). Our proof relies on relating the class group L-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke. The main technical contribution is the uniform sup norm bound for Eisenstein series E(z, 1/2 + it) ≪ε y1/2(|t| + 1)1/3+ε, y ≫ 1, extending work of Blomer and Titchmarsh. Finally, we propose a uniform version of the sup norm conjecture for Eisenstein series.
UR - http://www.scopus.com/inward/record.url?scp=85096200541&partnerID=8YFLogxK
U2 - 10.1515/forum-2019-0173
DO - 10.1515/forum-2019-0173
M3 - Journal article
AN - SCOPUS:85096200541
VL - 33
SP - 39
EP - 57
JO - Forum Mathematicum
JF - Forum Mathematicum
SN - 0933-7741
IS - 1
ER -
ID: 256678787