Prime numbers with a certain extremal type property by Edward Tutaj

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一类自守L-函数的零点密度估计(Zero density estimates of a kind of automorphic L-function) by DAIJinhui(代金辉), LIUHeng(刘恒)

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Some conjectures on the zeros of approximates to the Riemann ≡-function and incomplete gamma functions by Haglund James

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Upper bounds for the moments of derivatives of Dirichlet L-functions by Sono Keiju

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Combinatorial Models of the Distribution of Prime Numbers by Vito Barbarani

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18.785 Analytic Number Theory, Spring 2007 by Kedlaya, Kiran

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On the density of some special primes by Friedlander John B., Shparlinski Igor E.

“…We show, under the Generalized Riemann Hypothesis, that a certain set of primes which is of importance for the theory of pseudorandom sequences is of positive relative density. …”
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Counting primes, groups and manifolds by Goldfeld, D, Lubotzky, A, Nikolov, N, Pyber, L

“…The most general case of this result relies on the Generalized Riemann Hypothesis but many special cases are unconditional. …”

Detecting squarefree numbers by Booker, A, Hiary, G, Keating, J

“…We present an algorithm, based on the explicit formula for L-functions and conditional on the generalized Riemann hypothesis, for proving that a given integer is squarefree with little or no knowledge of its factorization. …”

Some Results on Harmonic Type Sums by Doğa Can Sertbaş, Haydar Göral

“…In particular, we give infinitely many asymptotics which are consequences of the Riemann hypothesis. We also give quantitative estimate for the moment function which counts non-integer hyperharmonic numbers. …”
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Error term of the mean value theorem for binary Egyptian fractions by Xiao Xuanxuan, Zhai Wenguang

“…An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained. The mean value in short interval is also considered.…”
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Cut-off phenomenon for the ax+b Markov chain over a finite field by Breuillard, E, Varjú, PP

“…Conditionally on the Riemann hypothesis for all Dedekind zeta functions, we show that the chain exhibits a cut-off phenomenon for most primes p and most values of a∈Fp×. …”

Supersymmetry and the Riemann zeros on the critical line by Ashok Das, Pushpa Kalauni

“…Namely, we construct a supersymmetric quantum mechanical model whose energy eigenvalues correspond to the Riemann zeta function in the strip 0<Res<1 (in the complex parameter space) and show that the zeros on the critical line arise naturally from the vanishing ground state energy condition in this model. Keywords: Riemann hypothesis, Supersymmetry, Riemann zeta function, Riemann zeros…”
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The distribution of quadratic residues and non-residues in the Goldwasser–Micali type of cryptosystem by Justus Benjamin

“…We provide unconditional results and conditional ones under the assumption of GRH (Generalized Riemann Hypothesis) on the distribution of quadratic residues and quadratic non-residues in ℤ/Nℤ$\mathbb {Z}/N\mathbb {Z}$, where N=pq$N= pq$ is an RSA modulus used in the Goldwasser–Micali cryptosystem. …”
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Average nonvanishing of Dirichlet L-functions atthe central point by Pratt, K

“…The Generalized Riemann Hypothesis implies that at least 50% of the central values L(1/2, χ)�are non-vanishing as χ ranges over primitive characters modulo q. …”

The average analytic rank of elliptic curves by Heath-Brown, D

“…All the results in this paper are conditional on the Riemann hypothesis for the L-functions of elliptic curves. …”

Harmonic numbers, harmonic series and zeta function by Sebbar Ahmed

“…This paper reviews, from different points of view, results on Bernoulli numbers and polynomials, the distribution of prime numbers in connexion with the Riemann hypothesis. We give an account on the theorem of G. …”
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On quadratic residue codes and hyperelliptic curves by David Joyner

“…We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''…”
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Scalar modular bootstrap and zeros of the Riemann zeta function by Nathan Benjamin, Cyuan-Han Chang

“…As a result, we rephrase the Riemann hypothesis purely as a statement about the asymptotic density of scalar operators in certain two-dimensional conformal field theories. …”
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Subgroup growth of lattices in semisimple Lie groups by Lubotzky, A, Nikolov, N

“…In the most general case our results depend on the Generalized Riemann Hypothesis for number fields but we can state the following unconditional theorem: Let $G$ be a simple Lie group of real rank at least 2, different than $D_4(\bbc)$, and let $\Gamma$ be any non-uniform lattice of $G$. …”