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Lifting of Maass forms to O(1,8n+1) and applications to the sup-norm problem

February 4 at 16:0017:00 CET

International Seminar on Automorphic Forms

Ameya Pitale (University of Oklahoma): Lifting of Maass forms to O(1,8n+1) and applications to the sup-norm problem

In a joint paper with Yingkun Li and Hiroaki Narita, we had constructed liftings from Maass forms with respect to SL_2(Z) to Maass forms on O(1,8n+1), which violated the Generalized Ramanujan conjecture. These were constructed via Borcherds theta lifts and we were able to give explicit formulas for their Fourier coefficients. In a recent joint work with Simon Marshall and Hiroaki Narita, we first computed the Petersson inner product of the lift using the Rallis inner product formula. This essentially involves an archimedean integral computation. These are usually very complicated and intractable, but in this case we are able to get an exact formula for the Petersson norm. Explicit formulas for the Fourier coefficients and Petersson norm are the essential ingredients of one of the approaches to obtain sup-norm bounds on these Maass forms. Investigations regarding sup-norm bounds for modular forms in the GL(2) case has been recently a very active area of research. Using the method mentioned above, as well as a pre-trace formula approach, we obtain the first sup-norm bounds results for these orthogonal groups.

https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits)

 

Details

Date:
February 4
Time:
16:00 – 17:00 CET
Website:
https://lykpi.github.io/ISoAF/

Organizers

Claire Burrin
Luis Garcia
Yingkun Li
Riccardo Zuffetti

Venue

Zoom