Algebraic twists of modular forms and Hecke orbits

By 'Etienne Fouvry, Emmanuel Kowalski, P. Michel. 2012

97 citations recorded by the source corpus.

We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistribution property for twisted Hecke orbits. This is done by exploiting the amplification method and the Riemann Hypothesis over finite fields, relying in particular on the ℓ-adic Fourier transform introduced by Deligne and studied by Katz and Laumon.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4f05bb2d9bf44469e449adfbe9c833b1d535d1c2

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In Algebra and Number Theory

1. P. Michel
2. Emmanuel Kowalski
3. V. Blomer
4. Djordje Milićević
5. W. Sawin
6. 'Etienne Fouvry
7. M. Young
8. R. Munshi

In Geometry and Topology

1. P. Michel
2. V. Blomer
3. Emmanuel Kowalski
4. Djordje Milićević
5. W. Sawin
6. 'Etienne Fouvry
7. M. Young
8. Akshay Venkatesh

In Mathematical Physics

1. P. Michel
2. Emmanuel Kowalski
3. V. Blomer
4. W. Sawin
5. Djordje Milićević
6. 'Etienne Fouvry
7. M. Young
8. R. Munshi

Citations in the corpus

• Bilinear forms with Kloosterman sums and applications (2015, methodology): “in any expression where some element zof Q¯ℓhas to be interpreted as a complex number, we mean to consider ι(z). We denote by c(F) the conductor of a constructible ℓ-adic sheaf Fon A1 Fq as defined in [FKM15a] (with adaptation to deal with sheaves which may not be middle-extensions). Recall that this”
• On moments of twisted L-functions (2014, background): “s usual kαk1 = X m |αm|, kαk2 = X m |αm|2 1/2 . The first part (5.1) and the third (5.5) have been proven by Fouvry, Kowalski and Michel in Theorems 1.17 and 1.16 (respectively) of [12] (building on [11]), in considerably greater generality. Thus it remains to prove the second part. 5.2. Generalsetup”