Averages of values of 𝐿-series

DOI10.1090/S0002-9939-2012-11506-0zbMath1331.11066MaRDI QIDQ4911818

Emre Alkan

Publication date: 20 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Gauss sumspecial valuesaverages\(L\)-seriescotangent sumEuler's totient functionJordan's totient function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gauss and Kloosterman sums; generalizations (11L05)

Related Items (13)

The twisted moments and distribution of values of Dirichlet \(L\)-functions at 1 ⋮ Sums of averages of generalized 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 ⋮ Certain weighted averages of generalized Ramanujan sums ⋮ A hybrid mean value of Dedekind sums and Kloosterman sums ⋮ Some notes on identities for Dirichlet \(L\)-functions ⋮ Series representations in the spirit of Ramanujan ⋮ Several expressions of Dirichlet \(L\)-function at positive integers ⋮ On the mean square value of the Dirichlet L-function at positive integers ⋮ On various mean values of Dirichlet L-functions ⋮ 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

• Values of Dirichlet \(L\)-functions, Gauss sums and trigonometric sums
• On the mean square average of special values of \(L\)-functions
• On Dirichlet \(L\)-functions with periodic coefficients and Eisenstein series
• Finite trigonometric sums and class numbers
• Some identities involving the Dirichlet L-function
• Lehmer 𝑘-tuples
• On the mean value of L(m,χ)L(n,χ) at positive integers m,n≥1
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