Academic literature on the topic 'Mathematics ; Number theory ; Analytic number theory'

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Journal articles on the topic "Mathematics ; Number theory ; Analytic number theory"

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Zaharescu, Alexandru. "Book Review: Analytic number theory." Bulletin of the American Mathematical Society 43, no. 02 (2006): 273–79. http://dx.doi.org/10.1090/s0273-0979-06-01084-6.

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Maslov, V. P. "Analytic number theory and disinformation." Mathematical Notes 100, no. 3-4 (2016): 568–78. http://dx.doi.org/10.1134/s0001434616090285.

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Zong, Chuanming. "Analytic Number Theory in China." Mathematical Intelligencer 32, no. 1 (2009): 18–25. http://dx.doi.org/10.1007/s00283-009-9087-1.

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Lucht, Lutz G. "CONTRIBUTIONS TO ABSTRACT ANALYTIC NUMBER THEORY." Quaestiones Mathematicae 24, no. 3 (2001): 309–22. http://dx.doi.org/10.1080/16073606.2001.9639220.

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CHEN, WEIYAN. "Analytic number theory for 0-cycles." Mathematical Proceedings of the Cambridge Philosophical Society 166, no. 1 (2017): 123–46. http://dx.doi.org/10.1017/s0305004117000767.

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AbstractThere is a well-known analogy between integers and polynomials over 𝔽q, and a vast literature on analytic number theory for polynomials. From a geometric point of view, polynomials are equivalent to effective 0-cycles on the affine line. This leads one to ask: Can the analogy between integers and polynomials be extended to 0-cycles on more general varieties? In this paper we study prime factorisation of effective 0-cycles on an arbitrary connected varietyVover 𝔽q, emphasizing the analogy between integers and 0-cycles. For example, inspired by the works of Granville and Rhoades, we prove that the prime factors of 0-cycles are typically Poisson distributed.
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Vardi, Ilan. "Integrals, an Introduction to Analytic Number Theory." American Mathematical Monthly 95, no. 4 (1988): 308. http://dx.doi.org/10.2307/2323562.

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Munshi, Ritabrata. "Analytic number theory in India during 2001–2010." Indian Journal of Pure and Applied Mathematics 50, no. 3 (2019): 719–38. http://dx.doi.org/10.1007/s13226-019-0351-6.

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Gelbart, S. "Book Review: Advanced analytic number theory: L-functions." Bulletin of the American Mathematical Society 45, no. 01 (2007): 169–76. http://dx.doi.org/10.1090/s0273-0979-07-01158-5.

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Karatsuba, A. A. "The Hilbert-Kamke problem in analytic number theory." Mathematical Notes of the Academy of Sciences of the USSR 41, no. 2 (1987): 155–61. http://dx.doi.org/10.1007/bf01138339.

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Hall, Richard R. "DUALITY IN ANALYTIC NUMBER THEORY (Cambridge Tracts in Mathematics 122)." Bulletin of the London Mathematical Society 30, no. 3 (1998): 318–19. http://dx.doi.org/10.1112/s0024609397224094.

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Dissertations / Theses on the topic "Mathematics ; Number theory ; Analytic number theory"

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Buchanan, Dan Matthews. "Analytic Number Theory and the Prime Number Theorem." Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1525451327211365.

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Maynard, James. "Topics in analytic number theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:3bf4346a-3efe-422a-b9b7-543acd529269.

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In this thesis we prove several different results about the number of primes represented by linear functions. The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(phi(q)log{x}) for some value C depending on log{x}/log{q}. Different authors have provided different estimates for C in different ranges for log{x}/log{q}, all of which give C>2 when log{x}/log{q} is bounded. We show in Chapter 2 that one can take C=2 provided that log{x}/log{q}> 8 and q is sufficiently large. Moreover, we also produce a lower bound of size x/(q^{1/2}phi(q)) when log{x}/log{q}>8 and is bounded. Both of these bounds are essentially best-possible without any improvement on the Siegel zero problem. Let k>1 and Pi(n) be the product of k linear functions of the form a_in+b_i for some integers a_i, b_i. Suppose that Pi(n) has no fixed prime divisors. Weighted sieves have shown that for infinitely many integers n, the number of prime factors of Pi(n) is at most r_k, for some integer r_k depending only on k. In Chapter 3 and Chapter 4 we introduce two new weighted sieves to improve the possible values of r_k when k>2. In Chapter 5 we demonstrate a limitation of the current weighted sieves which prevents us proving a bound better than r_k=(1+o(1))klog{k} for large k. Zhang has shown that there are infinitely many intervals of bounded length containing two primes, but the problem of bounded length intervals containing three primes appears out of reach. In Chapter 6 we show that there are infinitely many intervals of bounded length containing two primes and a number with at most 31 prime factors. Moreover, if numbers with up to 4 prime factors have `level of distribution' 0.99, there are infinitely many integers n such that the interval [n,n+90] contains 2 primes and an almost-prime with at most 4 prime factors.
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Guo, Charng Rang. "On analytic number theory." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357394.

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Dyke, Steven Douglas. "Topics in analytic number theory." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334817.

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Irving, Alastair James. "Topics in analytic number theory." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:40f5511c-af6b-4215-b1ab-97f203e8936b.

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In this thesis we prove several results in analytic number theory. 1. We show that there exist 3-digit palindromic primes in base b for a set of b having density 1 and that if b is sufficiently large then there is a $3$-digit palindrome in base b having precisely two prime factors. 2. We prove various estimates for averages of sums of Kloosterman fractions over primes. The first of these improves previous results of Fouvry-Shparlinski and Baker. 3. By using the q-analogue of van der Corput's method to estimate short Kloosterman sums we study the divisor function in an arithmetic progression to modulus q. We show that the expected asymptotic formula holds for a larger range of q than was previously known, provided that q has a certain factorisation. 4. Let ‖x‖ denote the distance from x to the nearest integer. We show that for any irrational α and any ϴ< 8/23 there are infinitely many n which are the product of two primes for which ‖nalpha‖ ≤ n <sup>-ϴ</sup>. 5. By establishing an improved level of distribution we study almost-primes of the form f(p,n) where f is an irreducible binary form over Z. 6. We show that for an irreducible cubic f ? Z[x] and a full norm form $mathbf N$ for a number field $K/Q$, satisfying certain hypotheses, the variety $$f(t)=mathbf N(x_1,ldots,x_k) e 0$$ satisfies the Hasse principle. Our proof uses sieve methods.
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Baker, Liam Bradwin. "Analytic methods in combinatorial number theory." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/98017.

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Thesis (MSc)--Stellenbosch University, 2015<br>ENGLISH ABSTRACT : Two applications of analytic techniques to combinatorial problems with number-theoretic flavours are shown. The first is an application of the real saddle point method to derive second-order asymptotic expansions for the number of solutions to the signum equation of a general class of sequences. The second is an application of more elementary methods to yield asymptotic expansions for the number of partitions of a large integer into powers of an integer b where each part has bounded multiplicity.<br>AFRIKAANSE OPSOMMING : Ons toon twee toepassings van analitiese tegnieke op kombinatoriese probleme met getalteoretiese geure. Die eerste is ’n toepassing van die reële saalpuntmetode wat tweede-orde asimptotiese uitbreidings vir die aantal oplossings van die ‘signum’ vergelyking vir ’n algemene klas van rye aflewer. Die tweede is ’n toepassing van meer elementêre metodes wat asimptotiese uitbreidings vir die aantal partisies van ’n groot heelgetal in magte van ’n heelgetal b, waar elke deel ’n begrensde meervoudigheid het, aflewer
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Powell, Kevin James. "Topics in Analytic Number Theory." BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/2084.

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The thesis is in two parts. The first part is the paper “The Distribution of k-free integers” that my advisor, Dr. Roger Baker, and I submitted in February 2009. The reader will note that I have inserted additional commentary and explanations which appear in smaller text. Dr. Baker and I improved the asymptotic formula for the number of k-free integers less than x by taking advantage of exponential sum techniques developed since the 1980's. Both of us made substantial contributions to the paper. I discovered the exponent in the error term for the cases k=3,4, and worked the case k=3 completely. Dr. Baker corrected my work for k=4 and proved the result for k=5. He then generalized our work into the paper as it now stands. We also discussed and both contributed to parts of section 3 on bounds for exponential sums. The second part represents my own work guided by my advisor. I study the zeros of derivatives of Dirichlet L-functions. The first theorem gives an analog for a result of Speiser on the zeros of ζ'(s). He proved that RH is equivalent to the hypothesis that ζ'(s) has no zeros with real part strictly between 0 and ½. The last two theorems discuss zero-free regions to the left and right for L^{(k)}(s,χ).
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Walker, Aled. "Topics in analytic and combinatorial number theory." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:0d48a697-fd7a-4aca-bebe-4806322bdbbd.

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In this thesis we consider three different issues of analytic number theory. Firstly, we investigate how residues modulo q may be expressed as products of small primes. In Chapter 1, we work in the regime in which these primes are less than q, and present some partial results towards an open conjecture of Erdös. In Chapter 2, we consider the kinder regime in which these primes are at most q<sup>C</sup> , for some constant C that is greater than 1. Here we reach an explicit version of Linnik's Theorem on the least prime in an arithmetic progression, saving that we replace 'prime' with 'product of exactly three primes'. The results of this chapter are joint with Prof. Olivier Ramaré. The next two chapters concern equidistribution modulo 1, specifically the notion that an infinite set of integers is metric poissonian. This strong notion was introduced by Rudnick and Sarnak around twenty years ago, but more recently it has been linked with concepts from additive combinatorics. In Chapter 3 we study the primes in this context, and prove that the primes do not enjoy the metric poissonian property, a theorem which, in passing, improves upon a certain result of Bourgain. In Chapter 4 we continue the investigation further, adapting arguments of Schmidt to demonstrate that certain random sets of integers, which are nearly as dense as the primes, are metric poissonian after all. The major work of this thesis concerns the study of diophantine inequalities. The use of techniques from Fourier analysis to count the number of solutions to such systems, in primes or in other arithmetic sets of interest, is well developed. Our innovation, following suggestions of Wooley and others, is to utilise the additive-combinatorial notion of Gowers norms. In Chapter 5 we adapt methods of Green and Tao to show that, even in an extremely general framework, Gowers norms control the number of solutions weighted by arbitrary bounded functions. We use this result to demonstrate cancellation of the Möbius function over certain irrational patterns.
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Mullen, Woodford Roger. "Partitions into prime powers and related divisor functions." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/1246.

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In this thesis, we will study a class of divisor functions: the prime symmetric functions. These are polynomials over Q in the so-called elementary prime symmetric functions, whose values lie in Z. The latter are defined on the nonnegative integers and take the values of the elementary symmetric functions applied to the multi-set of prime factors (with repetition) of an integer n. Initially we look at basic properties of prime symmetric functions, and consider analogues of questions posed for the usual sum of proper divisors function, such as those concerning perfect numbers or Aliquot sequences. We consider the inverse question of when, and in how many ways a number $n$ can be expressed as f(m) for certain prime symmetric functions f. Then we look at asymptotic formulae for the average orders of certain fundamental prime symmetric functions, such as the arithmetic function whose value at n is the sum of k-th powers of the prime divisors (with repetition) of n. For these last functions in particular, we also look at statistical results by comparing their distribution of values with the distribution of the largest prime factor dividing n. In addition to average orders, we look at the modular distribution of prime symmetric functions, and show that for a fundamental class, they are uniformly distributed over any fixed modulus. Then our focus shifts to the related area of partitions into prime powers. We compute the appropriate asymptotic formulae, and demonstrate important monotonicity properties. We conclude by looking at iteration problems for some of the simpler prime symmetric functions. In doing so, we consider the empirical basis for certain conjectures, and are left with many open problems.
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Wang, Stephen. "Zeta Function Regularization and its Relationship to Number Theory." Digital Commons @ East Tennessee State University, 2021. https://dc.etsu.edu/etd/3895.

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While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to zeta function regularization and explore more fully the relationship between operators in physics and classical zeta functions of mathematics. In so doing, we highlight intriguing connections to number theory that arise.
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Books on the topic "Mathematics ; Number theory ; Analytic number theory"

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P. D. T. A. Elliott. Duality in analytic number theory. Cambridge University Press, 1997.

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Analytic number theory: An introductory course. World Scientific, 2005.

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Shparlinski, Igor. Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness. Birkhäuser Basel, 2003.

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Paul, Sally, ed. Number, shape, and symmetry: An introduction to number theory, geometry, and group theory. A K Peters, 2012.

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Hejhal, Dennis A. Emerging Applications of Number Theory. Springer New York, 1999.

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1944-, Halter-Koch Franz, ed. Non-unique factorizations: Algebraic, combinatorial and analytic theory. CRC Press, 2005.

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Pearls of discrete mathematics. Taylor & Francis, 2009.

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Erickson, Martin J. Pearls of discrete mathematics. Taylor & Francis, 2009.

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Preda, Mihăilescu, and SpringerLink (Online service), eds. Contributions in Analytic and Algebraic Number Theory: Festschrift for S. J. Patterson. Springer Science+Business Media, LLC, 2012.

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Maria, Piacentini Cattaneo Giulia, Ciliberto C. (Ciro) 1950-, and SpringerLink (Online service), eds. Elementary Number Theory, Cryptography and Codes. Springer Berlin Heidelberg, 2009.

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Book chapters on the topic "Mathematics ; Number theory ; Analytic number theory"

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Anglin, W. S. "Analytic Number Theory." In Kluwer Texts in the Mathematical Sciences. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0285-8_7.

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Heath-Brown, Roger. "Rational Points and Analytic Number Theory." In Progress in Mathematics. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8170-8_2.

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Miyake, Katsuya. "Some Aspects of Interactions between Algebraic Number Theory and Analytic Number Theory." In Developments in Mathematics. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3675-5_14.

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Rashed, Roshdi. "Number Theory and Combinatorial Analysis." In The Development of Arabic Mathematics: Between Arithmetic and Algebra. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-3274-1_5.

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Deninger, Christopher. "Evidence for a Cohomological Approach to Analytic Number Theory." In First European Congress of Mathematics. Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-9110-3_16.

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Michel, Philippe. "Analytic Number Theory and Families of Automorphic 𝐿-functions." In IAS/Park City Mathematics Series. American Mathematical Society, 2007. http://dx.doi.org/10.1090/pcms/012/05.

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Deninger, Christopher. "Evidence for a Cohomological Approach to Analytic Number Theory." In First European Congress of Mathematics Paris, July 6–10, 1992. Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-9328-2_16.

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Deninger, Christopher. "On the Nature of the “Explicit Formulas” in Analytic Number Theory — A Simple Example." In Developments in Mathematics. Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3675-5_7.

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Lang, Serge. "Extension of Analytic Number Theory and the Theory of Regularized Harmonic Series from Dirichlet Series to Bessel Series." In Springer Collected Works in Mathematics. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4614-6325-2_5.

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Freitag, Eberhard, and Rolf Busam. "Analytic Number Theory." In Complex Analysis. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-93983-2_8.

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Conference papers on the topic "Mathematics ; Number theory ; Analytic number theory"

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Sotiropoulos, Megaklis Th, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Stochastic-Conceptual Models Applied to Number Theory." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636750.

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Todd, William. "The Theory of Molecular Dispersion in Flowing Fluids: An Analytic Solution of the Navier-Stokes Equations." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57269.

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This development is a description of the transport of mass, energy and momentum in flowing viscous fluids at the molecular level; and results in: • A thermostatistical link between Reynolds’ number and momentum and free energy, • A wave characterization of the behavior of flowing fluids using the forces of attraction between molecules as a basis, • Calculation of the velocity components in flowing fluids for all Reynolds’ numbers greater than 535; thus defining a mathematical theory of turbulence, • An analytic solution of the Navier-Stokes equations for incompressible fluids in 3-dimensions. The following steps lead to the solution: • Definition of the fluid Model, • A re-characterization of Reynolds’ number in terms of momentum and free energy, • Calculation of the shear and circulatory components of velocity, • Transformation of the Navier-Stokes equations into the curvilinear coordinates of the intermolecular force waves, • Using the transformed equations to calculate the velocity components and Pressure-wave front resulting from the current, • Corroboration of the theoretical results with: a) wave fronts as manifest in the behavior of sails in uniform flow, b) boundary layer definition/behavior compared to theoretical and empirical developments of Schlichting and others, and c) empirical results for forces measured in the OCEANIC/DeepStar high Re beam-tow tests.
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Nagasaka, Kenji. "Analytic Number Theory and Related Topics." In Proceedings of the Conference. WORLD SCIENTIFIC, 1993. http://dx.doi.org/10.1142/9789814535380.

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Wang, Jinrui. "Application of Analytic Number Theory in Bioinformatics." In 2017 5th International Conference on Frontiers of Manufacturing Science and Measuring Technology (FMSMT 2017). Atlantis Press, 2017. http://dx.doi.org/10.2991/fmsmt-17.2017.63.

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TSUKADA, HARUO. "A GENERAL MODULAR RELATION IN ANALYTIC NUMBER THEORY." In Proceedings of the 4th China-Japan Seminar. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812770134_0009.

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TSUKADA, HARUO. "Errata to: "A GENERAL MODULAR RELATION IN ANALYTIC NUMBER THEORY"." In Proceedings of the 5th China-Japan Seminar. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814289924_0011.

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Bethune, Iain. "PrimeGrid: a Volunteer Computing Platform for Number Theory." In Annual International Conference on Computational Mathematics, Computational Geometry & Statistics. Global Science and Technology Forum (GSTF), 2015. http://dx.doi.org/10.5176/2251-1911_cmcgs15.43.

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Simsek, Yilmaz. "Preface on the "3rd symposium on generating functions of special numbers and polynomials and their applications"." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756133.

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Simsek, Yilmaz, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Preface of the “2nd Symposium on Generating Functions of Special Numbers and Polynomials and their Applications”." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637755.

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Simsek, Yilmaz, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Symposium on Generating Functions of Special Numbers and Polynomials and their Applications." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3497832.

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Reports on the topic "Mathematics ; Number theory ; Analytic number theory"

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Dunlap, Brett I., Shashi P. Karna, and Rajendra R. Zope. Dipole Moments From Atomic-Number-Dependent Potentials in Analytic Density-Functional Theory. Defense Technical Information Center, 2010. http://dx.doi.org/10.21236/ada522802.

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