Log in

Relevant bibliographies by topics / Proof ;Beal Conjecture: Number theory / Journal articles

To see the other types of publications on this topic, follow the link: Proof ;Beal Conjecture: Number theory.

Journal articles on the topic 'Proof ;Beal Conjecture: Number theory'

Author: Grafiati

Published: 5 June 2025

Last updated: 15 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Proof ;Beal Conjecture: Number theory.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Mohammed, Ghanim. "A SHORT ELEMENTARY PROOF OF THE BEAL CONJECTURE WITH DEDUCTION OF THE FERMAT LAST THEOREM." GLOBAL JOURNAL OF ADVANCED ENGINEERING TECHNOLOGIES AND SCIENCES 8, no. 1 (2021): 1–16. https://doi.org/10.5281/zenodo.4568087.

Full text

Abstract:

The present short paper, which is an amelioration of my previous article “confirmation of the Beal-Brun-Tijdeman-Zagier conjecture” published by the GJETS in 20/11/2019 [15], confirms the Beal’s conjecture, remained open since 1914 and saying that:       The proof uses elementary tools of mathematics, such as the L’Hôpital rule, the Bolzano-Weierstrass theorem, the intermediate value theorem and the growth properties of certain elementary functions. The proof uses also the Catalan-Mihailescu theorem [18] [19] and some methods developed in my paper o

APA, Harvard, Vancouver, ISO, and other styles

2

Earnest, A. G. "Exponents of the class groups of imaginary Abelian number fields." Bulletin of the Australian Mathematical Society 35, no. 2 (1987): 231–46. http://dx.doi.org/10.1017/s0004972700013198.

Full text

Abstract:

It is a classical result, deriving from the Gaussian theory of genera of integral binary quadratic forms, that there exist only finitely many imaginary quadratic fields for which the ideal class group is a group of exponent two. This finiteness has been shown to extend to all those totally imaginary quadratic extensions of any fixed totally real algebraic number field. In this paper we put forward the conjecture that there exist only finitely many imaginary abelian algebraic number fields which have ideal class groups of exponent two, and we examine the extent to which existing methods can be

APA, Harvard, Vancouver, ISO, and other styles

3

Marshall, Stephen M. "An All-Inclusive Proof of Beal’s Conjecture." Bulletin of Society for Mathematical Services and Standards 7 (September 2013): 17–22. http://dx.doi.org/10.18052/www.scipress.com/bsmass.7.17.

Full text

Abstract:

This paper presents a complete and exhaustive proof of the Beal Conjecture. The approach to this proof uses the Fundamental Theorem of Arithmetic as the basis for the proof of the Beal Conjecture. The Fundamental Theorem of Arithmetic states that every number greater than 1 is either prime itself or is unique product of prime numbers. The prime factorization of every number greater than 1 is used throughout every section of the proof of the Beal Conjecture. Without the Fundamental Theorem of Arithmetic, this approach to proving the Beal Conjecture would not be possible.

APA, Harvard, Vancouver, ISO, and other styles

4

Stanojevic, Slobodan. "Beal Conjecture." Bulletin of Society for Mathematical Services and Standards 14 (June 2015): 7–27. http://dx.doi.org/10.18052/www.scipress.com/bsmass.14.7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Huicochea, Mario. "A proof of a conjecture of Lev." International Journal of Number Theory 14, no. 10 (2018): 2583–97. http://dx.doi.org/10.1142/s1793042118501543.

Full text

Abstract:

We say that a set of the form [Formula: see text] for some [Formula: see text] is an interval. For a nonempty finite subset [Formula: see text] of [Formula: see text] and [Formula: see text], Vsevolod Lev proved in [Optimal representations by sumsets and subset sums, J. Number Theory 62(1) (1997) 127–143] some results about the existence of long intervals contained in the [Formula: see text]-fold iterated sumset of [Formula: see text]. Furthermore, in the same paper, he proposed a conjecture [Optimal representations by sumsets and subset sums, J. Number Theory 62(1) (1997) 127–143, Conjecture

APA, Harvard, Vancouver, ISO, and other styles

6

Daw, Christopher, and Jinbo Ren. "Applications of the hyperbolic Ax–Schanuel conjecture." Compositio Mathematica 154, no. 9 (2018): 1843–88. http://dx.doi.org/10.1112/s0010437x1800725x.

Full text

Abstract:

In 2014, Pila and Tsimerman gave a proof of the Ax–Schanuel conjecture for the$j$-function and, with Mok, have recently announced a proof of its generalization to any (pure) Shimura variety. We refer to this generalization as the hyperbolic Ax–Schanuel conjecture. In this article, we show that the hyperbolic Ax–Schanuel conjecture can be used to reduce the Zilber–Pink conjecture for Shimura varieties to a problem of point counting. We further show that this point counting problem can be tackled in a number of cases using the Pila–Wilkie counting theorem and several arithmetic conjectures. Our

APA, Harvard, Vancouver, ISO, and other styles

7

Gica, Alexandru. "The Proof of a Conjecture of Additive Number Theory." Journal of Number Theory 94, no. 1 (2002): 80–89. http://dx.doi.org/10.1006/jnth.2001.2731.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Skutin, Alexander. "Proof of a conjecture of Wiegold." Journal of Algebra 526 (May 2019): 1–5. http://dx.doi.org/10.1016/j.jalgebra.2019.02.002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Hart, Bradd. "A proof of morley's conjecture." Journal of Symbolic Logic 54, no. 4 (1989): 1346–58. http://dx.doi.org/10.1017/s0022481200041128.

Full text

Abstract:

In the 1960's, it was conjectured that a complete first order theory in a countable language would have a nondecreasing spectrum on uncountable cardinals. This conjecture became known as Morley's conjecture. Shelah has proved this in [10]. The intent of this paper is to give a different proof which resembles a more naive way of approaching this theorem.Let I(T, λ) = the number of nonisomorphic models of T in cardinality λ. We prove:Theorem 0.1. If T is a complete countable first order theory then for ℵ0 < κ < λ, I(T,K) ≤ I(T, λ).In some sense, one can view Shelah's work on the classifica

APA, Harvard, Vancouver, ISO, and other styles

10

Vong, Seak-Weng, and Xiao-Qing Jin. "Proof of Böttcher and Wenzel's Conjecture." Operators and Matrices, no. 3 (2008): 435–42. http://dx.doi.org/10.7153/oam-02-26.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Zaman, Budee U. "GROUNDBREAKING PROOF FOR GOLDBACH’S CONJECTURE VERIFICATION WITH MATHEMATICAL INDUCTIONFORMULA." Journal of Advance Research in Mathematics And Statistics (ISSN 2208-2409) 11, no. 1 (2024): 90–98. http://dx.doi.org/10.61841/k7twx960.

Full text

Abstract:

This document presents a novel examination of the Goldbach Conjecture, a prominent and long-standing problem in number theory first proposed by Christian Goldbach in 1742. Our investigation offers a straightforward yet remarkable explanation for how even numbers greater than 2 can invariably be expressed as the sum of two prime numbers. Through a comprehensive analysis grounded in fundamental number theory and innovative methodologies, we demonstrate that every even number above 2 can be represented in this manner. Our approach simplifies understanding and opens new avenues for further researc

APA, Harvard, Vancouver, ISO, and other styles

12

Fraser, Robert, and James Wright. "The local sum conjecture in two dimensions." International Journal of Number Theory 16, no. 08 (2020): 1667–99. http://dx.doi.org/10.1142/s1793042120500888.

Full text

Abstract:

The local sum conjecture is a variant of some of Igusa’s questions on exponential sums put forward by Denef and Sperber. In a remarkable paper by Cluckers, Mustata and Nguyen, this conjecture has been established in all dimensions, using sophisticated, powerful techniques from a research area blending algebraic geometry with ideas from logic. The purpose of this paper is to give an elementary proof of this conjecture in two dimensions which follows Varčenko’s treatment of Euclidean oscillatory integrals based on Newton polyhedra for good coordinate choices. Another elementary proof is given by

APA, Harvard, Vancouver, ISO, and other styles

13

FARKAS, GAVRIL, and ANGELA ORTEGA. "HIGHER RANK BRILL–NOETHER THEORY ON SECTIONS OF K3 SURFACES." International Journal of Mathematics 23, no. 07 (2012): 1250075. http://dx.doi.org/10.1142/s0129167x12500759.

Full text

Abstract:

We discuss the role of K3 surfaces in the context of Mercat's conjecture in higher rank Brill–Noether theory. Using liftings of Koszul classes, we show that Mercat's conjecture in rank 2 fails for any number of sections and for any gonality stratum along a Noether–Lefschetz divisor inside the locus of curves lying on K3 surfaces. Then we show that Mercat's conjecture in rank 3 fails even for curves lying on K3 surfaces with Picard number 1. Finally, we provide a detailed proof of Mercat's conjecture in rank 2 for general curves of genus 11, and describe explicitly the action of the Fourier–Muk

APA, Harvard, Vancouver, ISO, and other styles

14

Currie, James, and Narad Rampersad. "A proof of Dejean’s conjecture." Mathematics of Computation 80, no. 274 (2011): 1063. http://dx.doi.org/10.1090/s0025-5718-2010-02407-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Efimov, Aleksander I. "A proof of the Kontsevich-Soǐbel'man conjecture." Sbornik: Mathematics 202, no. 4 (2011): 527–46. http://dx.doi.org/10.1070/sm2011v202n04abeh004154.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Mozzochi, C. J. "A proof of Sarnak's golden mean conjecture." Journal of Number Theory 214 (September 2020): 56–62. http://dx.doi.org/10.1016/j.jnt.2020.02.005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Moerdijk, I., and J. J. C. Vermeulen. "Proof of a conjecture of A. Pitts." Journal of Pure and Applied Algebra 143, no. 1-3 (1999): 329–38. http://dx.doi.org/10.1016/s0022-4049(98)00118-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Almkvist, Gert. "Proof of a conjecture about unimodal polynomials." Journal of Number Theory 32, no. 1 (1989): 43–57. http://dx.doi.org/10.1016/0022-314x(89)90096-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Rajeswari, K. N. "Standard monomial theoretic proof of prv conjecture." Communications in Algebra 19, no. 2 (1991): 347–425. http://dx.doi.org/10.1080/00927879108824145.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Yinbin, Lei, and Luo Maokang. "A Proof of Plotkin's Conjecture." Fundamenta Informaticae 92, no. 3 (2009): 301–6. http://dx.doi.org/10.3233/fi-2009-0076.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

CHMUTOV, S. "A PROOF OF THE MELVIN–MORTON CONJECTURE AND FEYNMAN DIAGRAMS." Journal of Knot Theory and Its Ramifications 07, no. 01 (1998): 23–40. http://dx.doi.org/10.1142/s0218216598000036.

Full text

Abstract:

The Melvin–Morton conjecture says how the Alexander–Conway knot invariant function can be read from the coloured Jones function. It has been proved by D. Bar-Natan and S. Garoufalidis. They reduced the conjecture to a statement about weight systems. The proof of the latter is the most difficult part of their paper. We give a new proof of the statement based on the Feynman diagram description of the primitive space of the Hopf algebra [Formula: see text] of chord diagrams.

APA, Harvard, Vancouver, ISO, and other styles

22

LALÍN, MATILDE N. "ON A CONJECTURE BY BOYD." International Journal of Number Theory 06, no. 03 (2010): 705–11. http://dx.doi.org/10.1142/s1793042110003174.

Full text

Abstract:

The aim of this note is to prove the Mahler measure identity m(x + x-1 + y + y-1 + 5) = 6m(x + x-1 + y + y-1 + 1) which was conjectured by Boyd. The proof is achieved by proving relationships between regulators of both curves.

APA, Harvard, Vancouver, ISO, and other styles

23

Ling, Xie. "Comment: Paper on the progress of pure mathematics "proof of 3x + 1 conjecture"." Annals of Mathematics and Physics 7, no. 2 (2024): 148–49. http://dx.doi.org/10.17352/amp.000117.

Full text

Abstract:

The unresolved problem in number theory: the 3x+1 problem, deeply loved by math enthusiasts. I saw a paper titled "Proof of 3x+1 Conjecture" in the Journal of Pure Mathematical Progress (ISSN Print: 2160-0368), and its proof was incorrect.

APA, Harvard, Vancouver, ISO, and other styles

24

Guo, Victor J. W. "Proof of Andrews' conjecture on a4φ3summation". Journal of Difference Equations and Applications 19, № 6 (2013): 1035–41. http://dx.doi.org/10.1080/10236198.2012.716048.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Thanatipanonda, Thotsaporn ‘Aek’. "A simple proof of Schmidt's conjecture." Journal of Difference Equations and Applications 20, no. 3 (2013): 413–15. http://dx.doi.org/10.1080/10236198.2013.838564.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Duc, Le Thanh. "Solution to the Birch and Swinnerton–dyer Conjecture." International Journal of Advanced Engineering and Management Research 10, no. 03 (2025): 184–89. https://doi.org/10.51505/ijaemr.2025.1209.

Full text

Abstract:

The Birch and Swinnerton–Dyer (BSD) conjecture is important in modern mathematical conjectures. Since the conjecture was born in 1960, many scientists have participated in solving this problem but have not been successful. The purpose of this article is to provide a way to prove this conjecture. The article's author solves it using pure mathematical theories and does not use mathematical software to find the solution. The proof process uses functions and related knowledge. In parallel, the properties of mappings and characteristics of isomorphisms are also important for clarifying the problem.

APA, Harvard, Vancouver, ISO, and other styles

27

von Känel, Rafael. "An effective proof of the hyperelliptic Shafarevich conjecture." Journal de Théorie des Nombres de Bordeaux 26, no. 2 (2014): 507–30. http://dx.doi.org/10.5802/jtnb.877.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Van de Weyer, Geert. "A proof of the Popov Conjecture for quivers." Journal of Algebra 274, no. 1 (2004): 373–86. http://dx.doi.org/10.1016/s0021-8693(03)00430-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Schmutz, Eric. "Proof of a conjecture of Erdös and Turán." Journal of Number Theory 31, no. 3 (1989): 260–71. http://dx.doi.org/10.1016/0022-314x(89)90073-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Ding, J. T. "A Proof of a Conjecture of C.L. Siegel." Journal of Number Theory 46, no. 1 (1994): 1–11. http://dx.doi.org/10.1006/jnth.1994.1001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Cao, Zhenfu, Shanzhi Mu, and Xiaolei Dong. "A New Proof of a Conjecture of Antoniadis." Journal of Number Theory 83, no. 2 (2000): 185–93. http://dx.doi.org/10.1006/jnth.1999.2489.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Freedman, Michael, and Vyacheslav Krushkal. "A homotopy+ solution to the A-B slice problem." Journal of Knot Theory and Its Ramifications 26, no. 02 (2017): 1740018. http://dx.doi.org/10.1142/s0218216517400181.

Full text

Abstract:

The A-B slice problem, a reformulation of the four-dimensional topological surgery conjecture for free groups, is shown to admit a link-homotopy[Formula: see text] solution. The proof relies on geometric applications of the group-theoretic [Formula: see text]-Engel relation. Implications for the surgery conjecture are discussed.

APA, Harvard, Vancouver, ISO, and other styles

33

Greither, Cornelius. "Fitting Ideals in Number Theory and Arithmetic." Jahresbericht der Deutschen Mathematiker-Vereinigung 123, no. 3 (2021): 153–81. http://dx.doi.org/10.1365/s13291-021-00233-5.

Full text

Abstract:

AbstractWe describe classical and recent results concerning the structure of class groups of number fields as modules over the Galois group. When presenting more modern developments, we can only hint at the much broader context and the very powerful general techniques that are involved, but we endeavour to give complete statements or at least examples where feasible. The timeline goes from a classical result proved in 1890 (Stickelberger’s Theorem) to a recent (2020) breakthrough: the proof of the Brumer-Stark conjecture by Dasgupta and Kakde.

APA, Harvard, Vancouver, ISO, and other styles

34

DEGTYAREV, ALEX. "OKA'S CONJECTURE ON IRREDUCIBLE PLANE SEXTICS II." Journal of Knot Theory and Its Ramifications 18, no. 08 (2009): 1065–80. http://dx.doi.org/10.1142/s0218216509007348.

Full text

Abstract:

We complete the proof of Oka's conjecture on the Alexander polynomial of an irreducible plane sextic. We also calculate the fundamental groups of irreducible sextics with a singular point adjacent to J10.

APA, Harvard, Vancouver, ISO, and other styles

35

Asok, Aravind. "Rationality problems and conjectures of Milnor and Bloch–Kato." Compositio Mathematica 149, no. 8 (2013): 1312–26. http://dx.doi.org/10.1112/s0010437x13007021.

Full text

Abstract:

AbstractWe show how the techniques of Voevodsky’s proof of the Milnor conjecture and the Voevodsky–Rost proof of its generalization the Bloch–Kato conjecture can be used to study counterexamples to the classical Lüroth problem. By generalizing a method due to Peyre, we produce for any prime number $\ell $ and any integer $n\geq 2$, a rationally connected, non-rational variety for which non-rationality is detected by a non-trivial degree $n$ unramified étale cohomology class with $\ell $-torsion coefficients. When $\ell = 2$, the varieties that are constructed are furthermore unirational and no

APA, Harvard, Vancouver, ISO, and other styles

36

Budur, Nero, and Ziyu Zhang. "Formality conjecture for K3 surfaces." Compositio Mathematica 155, no. 5 (2019): 902–11. http://dx.doi.org/10.1112/s0010437x19007206.

Full text

Abstract:

We give a proof of the formality conjecture of Kaledin and Lehn: on a complex projective K3 surface, the differential graded (DG) algebra$\operatorname{RHom}^{\bullet }(F,F)$is formal for any sheaf$F$polystable with respect to an ample line bundle. Our main tool is the uniqueness of the DG enhancement of the bounded derived category of coherent sheaves. We also extend the formality result to derived objects that are polystable with respect to a generic Bridgeland stability condition.

APA, Harvard, Vancouver, ISO, and other styles

37

Guo, Victor J. W., Guo-Shuai Mao, and Hao Pan. "Proof of a conjecture involving Sun polynomials." Journal of Difference Equations and Applications 22, no. 8 (2016): 1184–97. http://dx.doi.org/10.1080/10236198.2016.1188088.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Burungale, Ashay, Francesc Castella, and Chan-Ho Kim. "A proof of Perrin-Riou’s Heegner point main conjecture." Algebra & Number Theory 15, no. 7 (2021): 1627–53. http://dx.doi.org/10.2140/ant.2021.15.1627.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Alexandrino, Marcos M., and Marco Radeschi. "Closure of singular foliations: the proof of Molino’s conjecture." Compositio Mathematica 153, no. 12 (2017): 2577–90. http://dx.doi.org/10.1112/s0010437x17007485.

Full text

Abstract:

In this paper we prove the conjecture of Molino that for every singular Riemannian foliation $(M,{\mathcal{F}})$, the partition $\overline{{\mathcal{F}}}$ given by the closures of the leaves of ${\mathcal{F}}$ is again a singular Riemannian foliation.

APA, Harvard, Vancouver, ISO, and other styles

40

Chua, Lynn, Benjamin Gunby, Soohyun Park, and Allen Yuan. "Proof of a conjecture of Guy on class numbers." International Journal of Number Theory 11, no. 04 (2015): 1345–55. http://dx.doi.org/10.1142/s1793042115500724.

Full text

Abstract:

It is well known that for any prime p ≡ 3 (mod 4), the class numbers of the quadratic fields [Formula: see text] and [Formula: see text] and h(-p), respectively, are odd. It is natural to ask whether there is a formula for h(p)/h(-p) modulo powers of 2. We show the formula h(p) ≡ h(-p)m(p) (mod 16), where m(p) is an integer defined using the "negative" continued fraction expansion of [Formula: see text]. Our result solves a conjecture of Richard Guy.

APA, Harvard, Vancouver, ISO, and other styles

41

ILINCA, L., and J. KAHN. "On the Number of 2-SAT Functions." Combinatorics, Probability and Computing 18, no. 5 (2009): 749–64. http://dx.doi.org/10.1017/s096354830900995x.

Full text

Abstract:

We give an alternative proof of a conjecture of Bollobás, Brightwell and Leader, first proved by Peter Allen, stating that the number of Boolean functions definable by 2-SAT formulae is $(1+o(1))2^{\binom{n+1}{2}}$. $(1+o(1))2^{\scurvy{n+1}{2}}$. One step in the proof determines the asymptotics of the number of ‘odd-blue-triangle-free’ graphs on n vertices.

APA, Harvard, Vancouver, ISO, and other styles

42

Zhou, Zhongqi. "A Proof of a Conjecture and Twenty-Five Conjectures in Number Theory." OALib 11, no. 09 (2024): 1–9. http://dx.doi.org/10.4236/oalib.1112171.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Bley, Werner, and Ruben Debeerst. "Algorithmic proof of the epsilon constant conjecture." Mathematics of Computation 82, no. 284 (2013): 2363–87. http://dx.doi.org/10.1090/s0025-5718-2013-02691-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Montagard, P. L., B. Pasquier, and N. Ressayre. "Two generalizations of the PRV conjecture." Compositio Mathematica 147, no. 4 (2011): 1321–36. http://dx.doi.org/10.1112/s0010437x10005233.

Full text

Abstract:

AbstractLet G be a complex connected reductive group. The Parthasarathy–Ranga Rao–Varadarajan (PRV) conjecture, which was proved independently by S. Kumar and O. Mathieu in 1989, gives explicit irreducible submodules of the tensor product of two irreducible G-modules. This paper has three aims. First, we simplify the proof of the PRV conjecture, then we generalize it to other branching problems. Finally, we find other irreducible components of the tensor product of two irreducible G-modules that appear for ‘the same reason’ as the PRV ones.

APA, Harvard, Vancouver, ISO, and other styles

45

LAISHRAM, SHANTA. "ON A CONJECTURE ON RAMANUJAN PRIMES." International Journal of Number Theory 06, no. 08 (2010): 1869–73. http://dx.doi.org/10.1142/s1793042110003848.

Full text

Abstract:

For n ≥ 1, the nth Ramanujan prime is defined to be the smallest positive integer Rn with the property that if x ≥ Rn, then [Formula: see text] where π(ν) is the number of primes not exceeding ν for any ν > 0 and ν ∈ ℝ. In this paper, we prove a conjecture of Sondow on upper bound for Ramanujan primes. An explicit bound of Ramanujan primes is also given. The proof uses explicit bounds of prime π and θ functions due to Dusart.

APA, Harvard, Vancouver, ISO, and other styles

46

KOHNEN, WINFRIED. "A SHORT NOTE ON FOURIER COEFFICIENTS OF HALF-INTEGRAL WEIGHT MODULAR FORMS." International Journal of Number Theory 06, no. 06 (2010): 1255–59. http://dx.doi.org/10.1142/s1793042110003484.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Zhang, Wen-Bin. "Extensions of Beurling's prime number theorem." International Journal of Number Theory 11, no. 05 (2015): 1589–616. http://dx.doi.org/10.1142/s1793042115400126.

Full text

Abstract:

Kahane provided a proof of a conjecture of Bateman and Diamond on Beurling generalized primes. The conjecture says that the L2-condition [Formula: see text] implies the PNT, i.e. π(x) ~ x/ log x. Recently, Schlage-Puchta and Vindas showed that Beurling's condition in the form of a Cesàro mean [Formula: see text] with γ > 3/2 implies the PNT as well. Both are extensions of the Beurling PNT. We now show that the condition [Formula: see text] implies the PNT and that [Formula: see text] with k ≥ 0 implies the PNT also, where [Formula: see text]These results cover the preceding forms and extend

APA, Harvard, Vancouver, ISO, and other styles

48

Dobner, Alexander. "A proof of Newman’s conjecture for the extended Selberg class." Acta Arithmetica 201, no. 1 (2021): 29–62. http://dx.doi.org/10.4064/aa200603-23-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Abrashkin, Victor. "Modified proof of a local analogue of the Grothendieck conjecture." Journal de Théorie des Nombres de Bordeaux 22, no. 1 (2010): 1–50. http://dx.doi.org/10.5802/jtnb.703.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Chen, William Y. C., and Ernest X. W. Xia. "Proof of a conjecture of Hirschhorn and Sellers on overpartitions." Acta Arithmetica 163, no. 1 (2014): 59–69. http://dx.doi.org/10.4064/aa163-1-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!