Concept

Ramanujan's sum

Related publications (6)

Some applications of smooth bilinear forms with Kloosterman sums

We revisit a recent bound of I. Shparlinski and T. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earlier resul ...

Maik Nauka/Interperiodica/Springer2017

On Moments Of Twisted L-Functions

Philippe Michel

We study the average of the product of the central values of two L-functions of modular forms f and g twisted by Dirichlet characters to a large prime modulus q. As our principal tools, we use spectral theory to develop bounds on averages of shifted convol ...

Johns Hopkins Univ Press2017

Bilinear forms with Kloosterman sums and applications

Philippe Michel

We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...

Annal Mathematics2017

An efficient deterministic test for Kloosterman sum zeros

Robert Granger

We propose a simple deterministic test for deciding whether or not a non-zero element

a \in \mathbb{F}_{2^n}

\mathbb{F}_{3^n}

is a zero of the corresponding Kloosterman sum over these fields, and analyse its complexity. The test seems to have been o ...

American Mathematical Society2014

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Philippe Michel

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...

European Mathematical Soc2014

Cryptographic Hash Functions in Groups and Provable Properties

Juraj Sarinay

We consider several "provably secure" hash functions that compute simple sums in a well chosen group (G,*). Security properties of such functions provably translate in a natural way to computational problems in G that are simple to define and possibly also ...

EPFL2011

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An efficient deterministic test for Kloosterman sum zeros

Robert Granger

We propose a simple deterministic test for deciding whether or not a non-zero element

a \in \mathbb{F}_{2^n}

\mathbb{F}_{3^n}

is a zero of the corresponding Kloosterman sum over these fields, and analyse its complexity. The test seems to have been o ...

American Mathematical Society2014