A converse theorem for Dirichlet L-functions

作者：Kaczorowski Jerzy^*; Molteni Giuseppe; Perelli Alberto

来源：Commentarii Mathematici Helvetici, 2010, 85(2): 463-483.

DOI：10.4171/CMH/202

• Dirichlet L-functions
• converse theorems
• Hamburger theorem
• Selberg class

It is known that the space of solutions (in a suitable class of Dirichlet series with continuation over C) of the functional equation of a Dirichlet L-function L(s, chi) has dimension >= 2 as soon as the conductor q of chi is at least 4. Hence the Dirichlet L-functions are not characterized by their functional equation for g >= 4. Here we characterize the conductors g such that for every primitive character chi (mod g), L (s, chi) is the only solution with an Euler product in the above space. It turns out that such conductors are of the form g = 2(a)3(b)m with any square-free m coprime to 6 and finitely many a and b.

• 出版日期2010