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UID:6841@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20200123T140000
DTEND;TZID=Europe/Paris:20200123T150000
DTSTAMP:20241120T202025Z
URL:https://www.i2m.univ-amu.fr/evenements/fundamental-fourier-coefficient
 s-of-siegel-modular-forms-soumya-das/
SUMMARY:Soumya Das (Indian Institute of Science\, Bangalore): Fundamental F
 ourier coefficients of Siegel modular forms - Soumya Das
DESCRIPTION:Soumya Das: Understanding the Fourier coefficients of Siegel mo
 dular forms which are "fundamantal" i.e. indexed by matrices with fundamen
 tal discriminant has many applications. Generalising A. Saha's work on thi
 s topic\, we show that if F is a non-zero (possibly non-cuspidal) vector-
 valued level one Siegel modular form of any degree\, then it has infinitel
 y many non-zero Fourier coefficients which are indexed by half-integral ma
 trices having odd\, square-free (and thus fundamental) discriminant. The p
 roof uses an induction argument in the setting of vector-valued modular fo
 rms. As an application of a variant of our result and utilising the work o
 f A. Pollack\, this implies an unconditional proof of Andrianov's conjectu
 re for genus 3\, i.e.\, shows the expected standard analytic properties o
 f the spinor L-function of a holomorphic cuspidal Siegel Hecke eigenform 
 of degree 3 and level one. If time permits\, we can discuss mod p version
 s of this\, and related results.\nThese are joint works with Siegfried Boe
 cherer.
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Soumya_Das-1.jpg
CATEGORIES:Séminaire,Représentations des Groupes Réductifs
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
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 e de Séminaire 304-306 (3ème étage):geo:0,0
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DTSTART:20191027T020000
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