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DTSTART:20190331T030000
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DTSTAMP:20260405T022942Z
UID:5ca2144ecb1d6840262340@ist.ac.at
DTSTART:20191017T113000
DTEND:20191017T123000
DESCRIPTION:Speaker: Naser Talebizadeh Sardari\nhosted by Timothy Browning\
 nAbstract: We introduce a smooth variance sum associated with a pair of po
 sitive definite symmetric integral matrices A_{m x m} and B_{n x n}\, wher
 e m\\geq n. By using the oscillator representation\, we give a formula for
  this variance sum in terms of a smooth sum over the square of a functiona
 l evaluated on the B-th Fourier coefficients of the vector-valued holomorp
 hic  Siegel modular forms which are Hecke eigenforms and obtained by the t
 heta transfer from O_{A_{m x m}}.  By using the Ramanujan bound on the Fou
 rier coefficients of the holomorphic cusp forms\, we give a sharp upper bo
 und on this variance when n=1. As applications\, we prove a  cutoff phenom
 enon for the probability that a unimodular lattice of dimension m represen
 ts a given even number. This gives an optimal upper bound on the sphere pa
 cking density of almost all even unimodular lattices. Furthermore\, we gen
 eralize the result of  Bourgain\, Rudnick and Sarnak\, and also give an op
 timal bound on the diophantine exponent of the p-integral points on any po
 sitive definite d-dimensional quadric\, where d\\geq 3. This improves the 
 best-known bounds due to  Ghosh\, Gorodnik\, and Nevo into an optimal boun
 d.
LOCATION:Heinzel Seminar Room / Office Bldg West (I21.EG.101)\, ISTA
ORGANIZER:boosthui@ist.ac.at
SUMMARY:Naser Talebizadeh Sardari: The Siegel variance formula for quadrati
 c forms
URL:https://talks-calendar.ista.ac.at/events/2076
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