JOURNAL BROWSE
Search
Advanced SearchSearch Tips
TWISTED QUADRATIC MOMENTS FOR DIRICHLET L-FUNCTIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
TWISTED QUADRATIC MOMENTS FOR DIRICHLET L-FUNCTIONS
LOUBOUTIN, STEPHANE R.;
  PDF(new window)
 Abstract
Given c, a positive integer, we set. , where is the set of the (f)/2 odd Dirichlet characters mod f > 2, with gcd(f, c) = 1. We point out several mistakes in recently published papers and we give explicit closed formulas for the f's such that their prime divisors are all equal to modulo c. As a Corollary, we obtain closed formulas for M(f, c) for c {1, 2, 3, 4, 5, 6, 8, 10}. We also discuss the case of twisted quadratic moments for primitive characters.
 Keywords
L-function;character;mean values;moments;
 Language
English
 Cited by
1.
On the twisted quadratic moment for Dirichlet L-functions, Journal of Number Theory, 2017, 174, 427  crossref(new windwow)
 References
1.
E. Alkan, On the mean square average of special values of L-functions, J. Number Theory 131 (2011), no. 8, 1470-1485 crossref(new window)

2.
E. Alkan, On the mean square average of special values of L-functions, J. Number Theory 131 (2011), no. 11, 2245. crossref(new window)

3.
E. Alkan, Values of Dirichlet L-functions, Gauss sums and trigonometric sums, Ramanujan J. 26 (2011), no. 3, 375-398. crossref(new window)

4.
E. Alkan, Averages of values of L-series, Proc. Amer. Math. Soc. 141 (2013), no. 4, 1161-1175.

5.
A. Bayad and A. Raouj, Mean values of L-functions and Dedekind sums, J. Number Theory 132 (2012), no. 8, 1645-1652. crossref(new window)

6.
H. Liu, On the mean values of Dirichlet L-functions, J. Number Theory 147 (2015), 172-183. crossref(new window)

7.
S. Louboutin, Quelques formules exactes pour des moyennes de fonctions L de Dirichlet, Canad. Math. Bull. 36 (1993), 190-196. crossref(new window)

8.
S. Louboutin, Quelques formules exactes pour des moyennes de fonctions L de Dirichlet, Canad. Math. Bull. 37 (1994), 89. crossref(new window)

9.
S. Louboutin, On the mean value of ${\mid}L(1,\;\chi){\mid}^{2}$ for odd primitive Dirichlet characters, Proc. Japan Acad. Ser. A Math. Sci. 75 (1999), no. 7, 143-145. crossref(new window)

10.
S. Louboutin, The mean value of ${\mid}{\kappa}(1,\;\chi){\mid}^{2}$ at positive rational integers ${\kappa}{\geq}1$, Colloq. Math. 90 (2001), no. 1, 69-76. crossref(new window)

11.
S. Louboutin, Mean values of L-functions and relative class numbers of cyclotomic fields, Publ. Math. Debrecen 78 (2011), no. 3-4, 647-658. crossref(new window)

12.
S. Louboutin, A twisted quadratic moment for Dirichlet L-functions, Proc. Amer. Math. Soc. 142 (2014), no. 5, 1539-1544. crossref(new window)

13.
R. Ma, Y. L. Zhang, and M. Grutzmann, Some Notes on Identities for Dirichlet L- functions, Acta Math. Sin. (Engl. Ser.) 30 (2014), no. 5, 747-754. crossref(new window)

14.
T. Okamoto and T. Onozuka, On various mean values of Dirichlet L-functions, Acta Arith. 167 (2015), no. 2, 101-115. crossref(new window)

15.
M.-G. Qi, A class of mean square formulas for L-functions, J. Tsinghua Univ. 31 (1991), no. 3, 34-41.

16.
H. Walum, An exact formula for an average of L-series, Illinois J. Math. 26 (1982), no. 1, 1-3.

17.
Z.Wu andW. Zhang, On the mean values of $L(1,\;\chi)$, Bull. Korean Math. Soc. 49 (2012), no. 6, 1303-1310. crossref(new window)

18.
P. T. Young, Rational series for multiple zeta and log gamma functions, J. Number Theory 133 (2011), no. 12, 3995-4009.

19.
W. P. Zhang, A note on a class of mean square values of L-functions, J. Northwest Univ. 20 (1990), no. 3, 9-12.