Equidistribution of signs for modular eigenforms of half integral weight

İNAM İ., Wiese G.

Archiv der Mathematik, cilt.101, sa.4, ss.331-339, 2013 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 101 Sayı: 4
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1007/s00013-013-0566-4
  • Dergi Adı: Archiv der Mathematik
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.331-339
  • Anahtar Kelimeler: Forms of half-integer weight, Fourier coefficients of automorphic forms, Sato-Tate equidistribution, Shimura lift
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

Let f be a cusp form of weight k + 1/2 and at most quadratic nebentype character whose Fourier coefficients a(n) are all real. We study an equidistribution conjecture of Bruinier and Kohnen for the signs of a(n). We prove this conjecture for certain subfamilies of coefficients that are accessible via the Shimura lift by using the Sato-Tate equidistribution theorem for integral weight modular forms. Firstly, an unconditional proof is given for the family {a(tp 2)}p, where t is a squarefree number and p runs through the primes. In this case, the result is in terms of natural density. To prove it for the family {a(tn 2)}n where t is a squarefree number and n runs through all natural numbers, we assume the existence of a suitable error term for the convergence of the Sato-Tate distribution, which is weaker than one conjectured by Akiyama and Tanigawa. In this case, the results are in terms of Dedekind-Dirichlet density. © 2013 Springer Basel.