Values of Dirichlet \(L\)-functions, Gauss sums and trigonometric sums
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Publication:409025
DOI10.1007/s11139-010-9292-8zbMath1287.11101OpenAlexW2002937794MaRDI QIDQ409025
Publication date: 12 April 2012
Published in: The Ramanujan Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11139-010-9292-8
(zeta (s)) and (L(s, chi)) (11M06) Gauss and Kloosterman sums; generalizations (11L05) Trigonometric and exponential sums (general theory) (11L03)
Related Items (27)
RAMANUJAN SUMS AND THE BURGESS ZETA FUNCTION ⋮ Trigonometric series and special values of \(L\)-functions ⋮ The twisted moments and distribution of values of Dirichlet \(L\)-functions at 1 ⋮ Distribution of averages of Ramanujan sums ⋮ On the mean square average of Dirichlet \(L\)-function over characters of odd parity in a special case ⋮ Ramanujan sums are nearly orthogonal to powers ⋮ Covering sumsets of a prime field and class numbers ⋮ Generalized Bernoulli numbers, cotangent power sums, and higher-order arctangent numbers ⋮ Some notes on identities for Dirichlet \(L\)-functions ⋮ Character analogue of the Boole summation formula with applications ⋮ Evaluations of a weighted average of Gauss sums ⋮ Periodic analogues of Dedekind sums and transformation formulas of Eisenstein series ⋮ Structural properties of Dirichlet series with harmonic coefficients ⋮ Averages of values of 𝐿-series ⋮ On linear combinations of special values of \(L\)-functions ⋮ On the mean square average of special values of \(L\)-functions ⋮ Series representations in the spirit of Ramanujan ⋮ On Dirichlet \(L\)-functions with periodic coefficients and Eisenstein series ⋮ Several expressions of Dirichlet \(L\)-function at positive integers ⋮ Explicit expressions for finite trigonometric sums ⋮ Character gamma functions and evaluation of series with Dirichlet \(L\)-value coefficients ⋮ Rational series for multiple zeta and log gamma functions ⋮ On the mean square value of the Dirichlet L-function at positive integers ⋮ On various mean values of Dirichlet L-functions ⋮ Unnamed Item ⋮ The mean value of the generalized Dirichlet L-functions with the weight of the Gauss sums ⋮ Special values of the Riemann zeta function capture all real numbers
Cites Work
- On Dirichlet \(L\)-functions with periodic coefficients and Eisenstein series
- Finite trigonometric sums and class numbers
- Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications
- A new class of theta-function identities originating in Ramanujan's notebooks
- Some Eisenstein series identities related to modular equations of the seventh order.
- Weighted trigonometric sums over a half-period
- DETERMINATIONS OF ANALOGUES OF GAUSS SUMS AND OTHER TRIGONOMETRIC SUMS
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