On the mean values of L-functions in orthogonal and symplectic families

Details On the mean values of L-functions in orthogonal and symplectic families On the mean values of L-functions in orthogonal and symplectic families

2006-12-13

arxiv.org/abs/math/0612348v2

Proc. London Math. Soc. 96 (2008), 335--366

Mathematics

Number Theory

Scientific paper

Hybrid Euler-Hadamard products have previously been studied for the Riemann zeta function on its critical line and for Dirichlet L-functions in the context of the calculation of moments and connections with Random Matrix Theory. According to the Katz-Sarnak classification, these are believed to represent families of L-function with unitary symmetry. We here extend the formalism to families with orthogonal & symplectic symmetry. Specifically, we establish formulae for real quadratic Dirichlet L-functions and for the L-functions associated with primitive Hecke eigenforms of weight 2 in terms of partial Euler and Hadamard products. We then prove asymptotic formulae for some moments of these partial products and make general conjectures based on results for the moments of characteristic polynomials of random matrices.

Affiliated with

Also associated with

No associations

Rating

On the mean values of L-functions in orthogonal and symplectic families does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the mean values of L-functions in orthogonal and symplectic families, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the mean values of L-functions in orthogonal and symplectic families will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-586115