On the parity of k-th powers modulo p. A generalization of a problem of Lehmer
Jean Bourgain, Todd Cochrane, Jennifer Paulhus, Christopher Pinner (2011)
Acta Arithmetica
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Jean Bourgain, Todd Cochrane, Jennifer Paulhus, Christopher Pinner (2011)
Acta Arithmetica
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Friedlander, John, Iwaniec, Henryk (1998)
Annals of Mathematics. Second Series
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Ramon M. Nunes (2016)
Acta Arithmetica
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We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.
Serra, Oriol, Zémor, Gilles (2000)
Integers
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Jitomirskaya, Svetlana Ya. (1999)
Annals of Mathematics. Second Series
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Bender, Edward A., Richmond, L.Bruce (1996)
The Electronic Journal of Combinatorics [electronic only]
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E. Bombieri, H. Iwaniec (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Todd Cochrane, Christopher Pinner, Jason Rosenhouse (2003)
Acta Arithmetica
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Bentkus, V., Götze, F. (1999)
Annals of Mathematics. Second Series
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Patterson, S.J. (2003)
Experimental Mathematics
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Borwein, J.M., Bradley, D.M., Broadhurst, D.J. (1997)
The Electronic Journal of Combinatorics [electronic only]
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Chang Leran, Li Xiaoxue (2016)
Open Mathematics
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In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and asymptotic formula for it.
Gautami Bhowmik, Jan-Christoph Schlage-Puchta (2010)
Acta Arithmetica
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Todd Cochrane, Jeremy Coffelt, Christopher Pinner (2005)
Acta Arithmetica
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