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SUMMARY:Ade Irma Suriajaya (Kyushu University)
DTSTART:20210615T080000Z
DTEND:20210615T083000Z
DTSTAMP:20260423T010928Z
UID:JENTE/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JENTE/35/">G
 oldbach representations and exceptional zeros of Dirichlet L-functions</a>
 \nby Ade Irma Suriajaya (Kyushu University) as part of Japan Europe Number
  Theory Exchange Seminar\n\n\nAbstract\nG. H. Hardy and J. E. Littlewood i
 n 1922 studied the number of representations of a positive number as a sum
  of prime numbers. They conjectured that all large even numbers can be wri
 tten as a sum of two odd primes and also conjectured an asymptotic formula
  for the number of representations. This conjecture gives a quantitative s
 tatement of the well-known Goldbach's conjecture. J. Fei in 2016 used a we
 aker form of this Hardy-Littlewood Goldbach's Conjecture and showed that w
 e could almost eliminate the possible existence of the Landau-Siegel zeros
  of Dirichlet L-functions associated with characters modulo q congruent to
  3 mod 4. To be more precise\, Fei showed that we can narrow the interval 
 which may contain a possible exceptional zero of the corresponding Dirichl
 et L-function. G. Bhowmik and K. Halupczok in a recent preprint extended F
 ei's result to all odd characters with a slightly weaker conjecture. Indep
 endently\, C. Jia in his recent preprint used a slightly different form of
  weak Hardy-Littlewood Goldbach's Conjecture to obtain results similar to 
 Bhowmik and Halupczok's. We extended the weak Hardy-Littlewood Goldbach's 
 Conjecture as close as possible to the original Hardy-Littlewood Goldbach'
 s Conjecture and improved the arguments to extend Fei\, Bhowmik and Halupc
 zok\, and Jia's results to all Dirichlet L-functions associated with real 
 quadratic characters. This is a joint work with Daniel A. Goldston.\n\nFol
 lowing Goldston's talk at an AIM seminar early last month\, J. Friedlander
  and H. Iwaniec further improved our result and succeeded in showing that 
 the weak Hardy-Littlewood Goldbach's Conjecture we used indeed implies tha
 t there are no Landau-Siegel zeros. As in Friedlander and Iwaniec's approa
 ch\, using an improved estimate on the prime number theorem for primes in 
 arithmetic progressions\, we are able to further improve our arguments to 
 obtain Friedlander and Iwaniec's result. In this talk\, I would like to ex
 plain the slightly different conjectures and approaches used in this study
  and introduce relevant results.\n
LOCATION:https://researchseminars.org/talk/JENTE/35/
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