Improving the Error Term in the Mean Value of in the Hyperelliptic Ensemble

[1]  A. Weil.  Sur les courbes algébriques et les variétés qui s'en déduisent , 1948 .

[2]  D. Hayes.  The expression of a polynomial as a sum of three irreducibles , 1966 .

[3]  M. Jutila,et al.  On the Mean Value of L(1/2, χ ) FW Real Characters , 1981 .

[4]  Dorian Goldfeld,et al.  Eisenstein series of 1/2-integral weight and the mean value of real DirichletL-series , 1985 .

[5]  Kannan Soundararajan,et al.  Demography of Cirsium vulgare in a grazing experiment. , 1994 .

[6]  P. Sarnak,et al.  Zeroes of zeta functions and symmetry , 1999 .

[7]  Nina C Snaith,et al.  Random Matrix Theory and L-Functions at s= 1/2 , 2000 .

[8]  J. P. Keating,et al.  Integral Moments of L‐Functions , 2002, math/0206018.

[9]  Z. Rudnick.  Traces of high powers of the Frobenius class in the hyperelliptic ensemble , 2008, 0811.3649.

[10]  The fluctuations in the number of points on a hyperelliptic curve over a finite field , 2008, 0804.0808.

[11]  Z. Rudnick,et al.  Statistics of the zeros of zeta functions in families of hyperelliptic curves over a finite field , 2008, Compositio Mathematica.

[12]  Matthew P. Young,et al.  The first moment of quadratic Dirichlet L-functions , 2008, 0804.4141.

[13]  Michael Rubinstein,et al.  Conjectures and Experiments Concerning the Moments of L(1/2, χ d ) , 2012, Exp. Math..

[14]  J. Keating,et al.  The mean value of L(12,χ) in the hyperelliptic ensemble , 2012, 1208.1131.

[15]  Z. Rudnick,et al.  Low-lying Zeros of Quadratic Dirichlet L-Functions, Hyper-elliptic Curves and Random Matrix Theory , 2012, 1208.5962.

[16]  Z. Rudnick,et al.  The variance of the number of prime polynomials in short intervals and in residue classes , 2012, 1204.0708.

[17]  Jacob Tsimerman,et al.  Metaplectic Ramanujan conjecture over function fields with applications to quadratic forms , 2010, 1008.0430.

[18]  J. Keating,et al.  Conjectures for the integral moments and ratios of L-functions over function fields , 2014, 1407.3099.

[19]  M. Rubinstein,et al.  Moments of zeta functions associated to hyperelliptic curves over finite fields , 2014, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.