The TME-EMT project: the bibliography
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  • Ahn, Jeoung-Hwan, & Kwon, Soun-Hi. 2014
       Some explicit zero-free regions for Hecke {$L$}-functions. J. Number Theory, 145, 433--473.
  • Axler, Christian. 2016
       New bounds for the prime counting function. Integers, 16, Paper No. A22, 15.
  • Axler, Christian. 2019
       On the sum of the first {$n$} prime numbers. J. Théor. Nombres Bordeaux, 31(2), 293--311.
  • Bach, E., & Sorenson, J. 1996
       Explicit bounds for primes in residue classes. Math. Comp., 65(216), 1717--1735.
  • Bachman, Gennady, & Rachakonda, Leelanand. 2001
       On a problem of Dobrowolski and Williams and the Pólya-Vinogradov inequality. Ramanujan J., 5(1), 65--71.
  • Backlund, R. J. 1918
       Über die Nullstellen der {\it Riemannschen Zetafunktion.} . Acta Math., 41, 345--375.
  • Backlund, R.J. 1914
       Sur les zéros de la fonction $\zeta(s)$ de Riemann. C. R. Acad. Sci., 158, 1979--1981.
  • Baker, R., Harman, G., & Pintz, J. 2001
       The difference between consecutive primes, III. Proc. London Math. Soc., 83(3), 532--562.
  • Balazard, M. 2012
       Elementary Remarks on Möbius' Function. Proceedings of the Steklov Intitute of Mathematics, 276, 33--39.
  • Bastien, G., & Rogalski, M. 2002
       Convexité, complète monotonie et inégalités sur les fonctions z\^eta et gamma, sur les fonctions des opérateurs de Baskakov et sur des fonctions arithmétiques. Canad. J. Math., 54(5), 916--944.
  • Bennett, M. 2001
       Rational approximation to algebraic numbers of small height: the Diophantine equation $|ax^n-by^n|=1$. J. reine angew. Math., 535, 1--49.
  • Bennett, Michael A., Martin, Greg, O'Bryant, Kevin, & Rechnitzer, Andrew. 2018
       Explicit bounds for primes in arithmetic progressions. Illinois J. Math., 62(1-4), 427--532.
  • Bennett, Michael A., Martin, Greg, O'Bryant, Kevin, & Rechnitzer, Andrew. 2021
       Counting zeros of Dirichlet {$L$}-functions. Math. Comp., 90(329), 1455--1482.
  • Berkane, D., Bordellès, O., & Ramaré, O. 2012
       Explicit upper bounds for the remainder term in the divisor problem. Math. of Comp., 81(278), 1025--1051.
  • Berment, P., & Ramaré, O. 2012
       Ordre moyen d'une fonction arithmétique par la méthode de convolution. Revue de la filière mathématiques (RMS), 122(1), 1--15.
  • Bombieri, E., & Pila, J. 1989
       The number of integral points on arcs and ovals. Duke Math. J., 59, 337--357.
  • Booker, A.R. 2006
       Quadratic class numbers and character sums. Math. Comp., 75(255), 1481--1492 (electronic).
  • Bordellès, O. 2002
       Explicit upper bounds for the average order of {$d_n(m)$} and application to class number. JIPAM. J. Inequal. Pure Appl. Math., 3(3), Article 38, 15 pp. (electronic).
  • Bordellés, O. 2005
       An explicit Mertens' type inequality for arithmetic progressions. J. Inequal. Pure Appl. Math., 6(3), paper no 67 (10p).
  • Bordellès, O. 2006
       An inequality for the class number. JIPAM. J. Inequal. Pure Appl. Math., 7(3), Article 87, 8 pp. (electronic).
  • Bordellès, O. 2012
       Arithmetic Tales. Universitext. Springer London Heidelberg New York Dordrecht.
  • Bordellès, Olivier. 2015
       Some explicit estimates for the Möbius function. J. Integer Seq., 18(11), Article 15.11.1, 13.
  • Bordignon, Matteo. 2021
       A Pólya-Vinogradov inequality for short character sums. Canad. Math. Bull., 64(4), 906--910.
  • Bordignon, Matteo, & Kerr, Bryce. 2020
       An explicit Pólya-Vinogradov inequality via partial Gaussian sums. Trans. Amer. Math. Soc., 373(9), 6503--6527.
  • Borwein, P., Ferguson, R., & Mossinghoff, M.J. 2008
       Sign changes in sums of the Liouville function. Math. Comp., 77(263), 1681--1694.
  • Brillhart, J., Lehmer, D.H., & Selfridge, J.L. 1975
       New primality crietria and factorizations for $2^m \pm 1$. Math. Comp., 29(130), 620--647.
  • Büthe, J. 2014
       A Brun-Titchmarsh inequality for weighted sums over prime numbers. Acta Arith., 166(3), 289--299.
  • Büthe, Jan. 2016
       Estimating {$\pi(x)$} and related functions under partial RH assumptions. Math. Comp., 85(301), 2483--2498.
  • Büthe, Jan. 2018
       An analytic method for bounding {$\psi(x)$}. Math. Comp., 87(312), 1991--2009.
  • Carneiro, Emanuel, Milinovich, Micah, & Soundararajan, Kannan. 2019
       Fourier optimization and prime gaps.
  • Cazaran, J., & Moree, P. 1999
       On a claim of Ramanujan in his first letter to Hardy. Expositiones Mathematicae, 17, 289--312. based on a lecture given 01-12-1997 by J. Cazaran at the Hardy symposium in Sydney.
  • Chen, Jingrun, & Wang, Tianze. 1989
       On the distribution of zeros of Dirichlet L-functions. J. Sichuan Univ., Nat. Sci. Ed., 26.
  • Cheng, Y., & Graham, S.W. 2004
       Explicit estimates for the Riemann zeta function. Rocky Mountain J. Math., 34(4), 1261--1280.
  • Chua, Kok Seng. 2005
       Real zeros of Dedekind zeta functions of real quadratic field. Math. Comput., 74(251), 1457--1470.
  • Cipolla, M. 1902
       La determinatzione assintotica dell`$n^{imo}$ numero primo. Matematiche Napoli, 3, 132--166.
  • Cipu, Mihai. 2015
       Further remarks on Diophantine quintuples. Acta Arith., 168(3), 201--219.
  • Coffey, M.W. 2006
       New results on the Stieltjes constants: asymptotic and exact evaluation. J. Math. Anal. Appl., 317(2), 603--612.
  • Cohen, H., & Dress, F. 1988
       Estimations numériques du reste de la fonction sommatoire relative aux entiers sans facteur carré. Prépublications mathématiques d'Orsay : Colloque de théorie analytique des nombres, Marseille, 73--76.
  • Cohen, H., Dress, F., & El Marraki, M. 1996
       Explicit estimates for summatory functions linked to the Möbius $\mu$-function. Univ. Bordeaux 1, Pré-publication(96-7).
  • Cohen, H., Dress, F., & El Marraki, M. 2007
       Explicit estimates for summatory functions linked to the Möbius {$\mu$}-function. Funct. Approx. Comment. Math., 37, 51--63.
  • Costa Pereira, N. 1989
       Elementary estimates for the Chebyshev function $\psi(X)$ and for the Möbius function $M(X)$. Acta Arith., 52, 307--337.
  • Cramer, H. 1936
       On the order of magnitude of the difference between consecutive prime numbers. Acta Arith., 2, 23--46.
  • Cully-Hugill, Michaela. 2021
       Primes between consecutive powers. arXiv preprint arXiv:2107.14468.
  • Cully-Hugill, Michaela, & Trudgian, Tim. 2021
       Two explicit divisor sums. Ramanujan J., 56(1), 141--149.
  • Daboussi, H., & Rivat, J. 2001
       Explicit upper bounds for exponential sums over primes. Math. Comp., 70(233), 431--447.
  • Daublebsky von Sterneck, R. 1902
       Ein Analogon zur additiven Zahlentheorie. Wien. Ber., 111, 1567--1601.
  • Davenport, H. 1937
       On some infinite series involving arithmetical functions. Quart. J. Math., Oxf. Ser., 8, 8--13.
  • De Koninck, Jean-Marie, & Letendre, Patrick. 2020
       New upper bounds for the number of divisors function. Colloq. Math., 162(1), 23--52.
  • Delange, Hubert. 1987
       Une remarque sur la dérivée logarithmique de la fonction z\^eta de Riemann. Colloq. Math., 53(2), 333--335.
  • Deléglise, M., & Rivat, J. 1996a
       Computing $\pi (x)$ : The Meissel, Lehmer, Lagarias, Miller, Odlyzko method. Math. Comp., 65(213), 235--245.
  • Deléglise, M., & Rivat, J. 1996b
       Computing the summation of the Möbius function. Exp. Math., 5(4), 291--295.
  • Deléglise, M., & Rivat, J. 1998
       Computing $\psi(x)$. Math. Comp., 67(224), 1691--1696.
  • Deléglise, Marc, & Nicolas, Jean-Louis. 2019a
       An arithmetic equivalence of the Riemann hypothesis. J. Aust. Math. Soc., 106(2), 235--273.
  • Deléglise, Marc, & Nicolas, Jean-Louis. 2019b
       The Landau function and the Riemann Hypothesis. J. Combinatorics and Numb. Th., 11(2), 45--95.
  • Deshouillers, J.-M, & Dress, F. 1988
       Sommes de diviseurs et structure multiplicative des entiers. Acta Arith., 49(4), 341--375.
  • Deshouillers, J.-M., te Riele, H.J.J., & Saouter, Y. 1998
       New experimental results concerning the Goldbach conjecture. In: Buhler, J.P. (ed), Algorithmic number theory. Lect. Notes Comput. Sci., no. 1423.
  • Diamond, H.G., & Erdös, P. 1980
       On sharp elementary prime number estimates. Enseign. Math., 26(3-4), 313--321.
  • Dress, F. 1983/84
       Théorèmes d'oscillations et fonction de Möbius. URL Sémin. Théor. Nombres, Univ. Bordeaux I, Exp. No 33, 33pp. .
  • Dress, F. 1993
       Fonction sommatoire de la fonction de Möbius 1. Majorations expérimentales. Exp. Math., 2(2).
  • Dress, F. 1999
       Discrépance des suites de Farey. J. Théor. Nombres Bordx., 11(2), 345--367.
  • Dress, F., & El Marraki, M. 1993
       Fonction sommatoire de la fonction de Möbius 2. Majorations asymptotiques élémentaires. Exp. Math., 2(2), 99--112.
  • Dudek, Adrian W. 2015
       On the Riemann hypothesis and the difference between primes. Int. J. Number Theory, 11(3), 771--778.
  • Dudek, Adrian W. 2016
       An explicit result for primes between cubes. Functiones et Approximatio Commentarii Mathematici, 55(2), 177--197.
  • Duras, J.-L. 1993
       Etude de la fonction nombre de façons de représenter un entier comme produit de k facteurs. URL Ph.D. thesis, Université de Limoges. .
  • Duras, J.-L., Nicolas, J.-L., & Robin, G. 1999
       Grandes valeurs de la fonction {$d_k$}. Pages 743--770 of: Number theory in progress, Vol. 2 (Zakopane-Kościelisko, 1997). Berlin: de Gruyter.
  • Dusart, P. 1998
       Autour de la fonction qui compte le nombre de nombres premiers. URL Ph.D. thesis, Limoges, . 173 pp.
  • Dusart, P. 1999a
       Inégalités explicites pour $\psi(X)$, $\theta(X)$, $\pi(X)$ et les nombres premiers. C. R. Math. Acad. Sci., Soc. R. Can., 21(2), 53--59.
  • Dusart, P. 1999b
       The $k$th prime is greater than $k(\ln k+\ln\ln k-1)$ for $k\geq 2$. Math. Comp., 68(225), 411--415.
  • Dusart, P. 2002
       Estimates for $\theta(x;k,\ell)$ for large values of $x$. Math. Comp., 71(239), 1137--1168.
  • Dusart, P. 2018
       Estimates of some functions over primes. Ramanujan J., 45(1), 227--251.
  • Dusart, Pierre. 2016
       Estimates of {$\psi,\theta$} for large values of {$x$} without the Riemann hypothesis. Math. Comp., 85(298), 875--888.
  • El Marraki, M. 1995
       Fonction sommatoire de la fonction $\mu$ de Möbius, majorations asymptotiques effectives fortes. J. Théor. Nombres Bordeaux, 7(2), 407–433.
  • El Marraki, M. 1996
       Majorations de la fonction sommatoire de la fonction $\frac{\mu(n)}n$. Univ. Bordeaux 1, Pré-publication(96-8).
  • Eum, Ick Sun, & Koo, Ja Kyung. 2015
       The Riemann hypothesis and an upper bound of the divisor function for odd integers. J. Math. Anal. Appl., 421(1), 917--924.
  • Faber, L., & Kadiri, H. 2015
       New bounds for $\psi(x)$. Math. Comp., 84(293), 1339--1357.
  • Fan, Kai. 2022
       An inequality for the distribution of numbers free of small prime factors. Integers, 22, Paper No. A26, 12.
  • Filaseta, M. 1990
       Short interval results for squarefree numbers. J. Number Theory, 35, 128--149.
  • Filaseta, M., & Trifonov, O. 1996
       The distribution of fractional parts with applications to gap results in number theory. Proc. Lond. Math. Soc., III. Ser., 73(2), 241--278.
  • Ford, K. 2000
       Zero-free regions for the Riemann zeta function. Proceedings of the Millenial Conference on Number Theory, Urbana, IL.
  • Ford, K. 2002
       Vinogradov's integral and bounds for the Riemannn zeta function. Proc. London Math. Soc., 85, 565--633.
  • Frolenkov, D. 2011
       A numerically explicit version of the Pólya-Vinogradov inequality. Mosc. J. Comb. Number Theory, 1(3), 25--41.
  • Frolenkov, D. A., & Soundararajan, K. 2013
       A generalization of the Pólya--Vinogradov inequality. Ramanujan J., 31(3), 271--279.
  • Gabcke, W. 1979
       Neue Herleitung und explizite Restabschaetzung der Riemann-Siegel-Formel. Ph.D. thesis, Mathematisch-Naturwissenschaftliche Fakultät der Georg-August-Universität zu Göttingen.
  • Gallagher, P.X. 1970
       A large sieve density estimate near $\sigma =1$. Invent. Math., 11, 329--339.
  • Gourdon, X., & Demichel, P. 2004
       The $10^{13}$ first zeros of the Riemann Zeta Function and zeros computations at very large height . URL http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeros1e13-1e24.pdf
  • Graham, S. W., & Kolesnik, G. 1991
       Van der Corput's Method of Exponential Sums. London Math. Soc. Lect. Note, no. 126. Cambridge University Press.
  • Granville, A., & Ramaré, O. 1996
       Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients. Mathematika, 43(1), 73--107.
  • Granville, A., & Soundararajan, K. 2003
       The distribution of values of $L(1,\chi)$. URL Geom. Func. Anal., 13(5), 992--1028. .
  • Granville, A., & Soundararajan, K. 2004
       Errata to: The distribution of values of $L(1,\chi)$, in GAFA 13:5 (2003). Geom. Func. Anal., 14(1), 245--246.
  • Granville, A., & Soundararajan, K. 2007
       Large character sums: pretentious characters and the Pólya-Vinogradov theorem. J. Amer. Math. Soc., 20(2), 357--384 (electronic).
  • Hall, R., & Tenenbaum, G. 1988
       Divisors. Cambridge Tracts in Mathematics, vol. 90. Cambridge: Cambridge University Press.
  • Hasanalizade, Elchin, Shen, Quanli, & Wong, Peng-Jie. 2021
       Counting zeros of Dedekind zeta functions. Math. Comp., 91(333), 277--293.
  • Hasanalizade, Elchin, Shen, Quanli, & Wong, Peng-Jie. 2022
       Counting zeros of the Riemann zeta function. J. Number Theory, 235, 219--241.
  • Helfgott, H.A. 2017
       $L^2$ bounds for tails of $\zeta(s)$ on a vertical line. URL .
  • Hiary, Ghaith A. 2016a
       An explicit hybrid estimate for {$L(1/2+it,\chi)$}. Acta Arith., 176(3), 211--239.
  • Hiary, Ghaith A. 2016b
       An explicit van der Corput estimate for {$\zeta(1/2+it)$}. Indag. Math. (N.S.), 27(2), 524--533.
  • Hurst, Greg. 2018
       Computations of the Mertens function and improved bounds on the Mertens conjecture. Math. Comp., 87(310), 1013--1028.
  • Huxley, M.N. 1996
       Area, Lattice Points and Exponential Sums. Oxford Science Pub.
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       Integer points close to a plane curve of class $C^n$. (Points entiers au voisinage d'une courbe plane de classe $C^n$.). Acta Arith., 69(4), 359--366.
  • Huxley, M.N., & Sargos, P. 2006
       Integer points in the neighborhood of a plane curve of class $C^n$. II. (Points entiers au voisinage d'une courbe plane de classe $C^n$. II.). Funct. Approximatio, Comment. Math., 35, 91--115.
  • Huxley, M.N., & Trifonov, O. 1996
       The square-full numbers in an interval. Math. Proc. Camb. Phil. Soc., 119, 201--208.
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       Two inequalities for the sum of the divisors functions. Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak., 7, 17--21.
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       On strong pseudoprimes to several bases. Math. Comp., 61(204), 915--926.
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       Explicit Burgess bound for composite moduli. Int. J. Number Theory, 17(10), 2207--2219.
  • Jang, Woo-Jin, & Kwon, Soun-Hi. 2014
       A note on Kadiri's explicit zero free region for Riemann zeta function. J. Korean Math. Soc., 51(6), 1291--1304.
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       Über die Gitterpunkte auf konvexen Kurven. Math. Z., 24, 500--518.
  • Kadiri, H. 2002
       Une région explicite sans zéros pour les fonctions {$L$ de Dirichlet}. URL Ph.D. thesis, Université Lille 1. .
  • Kadiri, H. 2005
       Une région explicite sans zéros pour la fonction $\zeta$ de Riemann. Acta Arith., 117(4), 303--339.
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       Short effective intervals containing primes in arithmetic progressions and the seven cube problem. Math. Comp., 77(263), 1733--1748.
  • Kadiri, H. 2009
       An explicit zero-free region for the Dirichlet {$L$}-functions. URL Being processed... .
  • Kadiri, H. 2012
       Explicit zero-free regions for Dedekind zeta functions. URL Int. J. Number Theory, 8(1), 125--147. .
  • Kadiri, H. 2013
       A zero density result for the Riemann zeta function. Acta Arith., 160(2), 185--200.
  • Kadiri, H., & Ng, N. 2012
       Explicit zero density theorems for Dedekind zeta functions. J. Number Theory, 132(4), 748--775.
  • Kadiri, Habiba, Lumley, Allysa, & Ng, Nathan. 2018
       Explicit zero density for the Riemann zeta function. J. Math. Anal. Appl., 465(1), 22--46.
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       On the order of the Mertens function. Experiment. Math., 13(4), 473--481.
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       On the average number of divisors of reducible quadratic polynomials. J. Number Theory, 180, 710--729.
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       On the difference {$\pi (x)-{\rm li}(x)$}. Acta Arith., 11, 397--410.
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       Separation of zeros of the Riemann zeta-function. Math. Comp., 20, 523--541.
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       On the distribution of zeros of the Riemann zeta-function. Proc. London Math. Soc. (3), 20, 303--320.
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