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Found 2 essays matching the above criteria.

1. 1. Low-lying zeroes of L-functions attached to modular forms

   University essay from Göteborgs universitet/Institutionen för matematiska vetenskaper

   Author : Alf Söderberg; [2024-03-22]
   Keywords : Number theory; L-functions; Modular forms; Newforms; Low-lying zeros; 1-level density; Density Conjecture; Ratios Conjecture.;

   Abstract : We study the family of L-functions attached to Hecke newforms of weight k and level N and their low-lying zeroes. First, we recall the Density Conjecture of Katz and Sarnak and how it predicts the behaviour of the low-lying zeroes of any natural family of L-functions. READ MORE

3. 2. The low-lying zeros of L-functions associated to non-Galois cubic fields

   University essay from Göteborgs universitet/Institutionen för matematiska vetenskaper

   Author : Victor Ahlquist; [2023-02-13]
   Keywords : Mathematics; number theory; cubic fields; L-functions; low-lying zeros; onelevel density; two-level density; phase transition.;

   Abstract : We study the low-lying zeros of Artin L-functions associated to non-Galois cubic number fields through their one- and two-level densities. In particular, we find new precise estimates for the two-level density with a power-saving error term. READ MORE