Mathematics of Computation最新文献

{"title":"A classification of genus 0 modular curves with rational points","authors":"None Rakvi","doi":"10.1090/mcom/3907","DOIUrl":"https://doi.org/10.1090/mcom/3907","url":null,"abstract":"Let <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E\"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding=\"application/x-tex\">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a non-CM elliptic curve defined over <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Q\"> <mml:semantics> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">Q</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbb {Q}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Fix an algebraic closure <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Q overbar\"> <mml:semantics> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mover> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">Q</mml:mi> </mml:mrow> <mml:mo accent=\"false\">¯<!-- ¯ --></mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">{overline {mathbb Q}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Q\"> <mml:semantics> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">Q</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathbb {Q}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We get a Galois representation <disp-formula content-type=\"math/mathml\"> [ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"rho Subscript upper E Baseline colon upper G a l left-parenthesis double-struck upper Q overbar slash double-struck upper Q right-parenthesis right-arrow upper G upper L 2 left-parenthesis ModifyingAbove double-struck upper Z With caret right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>ρ<!-- ρ --></mml:mi> <mml:mi>E</mml:mi> </mml:msub> <mml:mo>:<!-- : --></mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi>G</mml:mi> <mml:mi>a</mml:mi> <mml:mi>l</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mover> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">Q</mml:mi> </mml:mrow> <mml:mo accent=\"false\">¯<!-- ¯ --></mml:mo> </mml:mover> </mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">Q</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo stretchy=\"false\">→<!-- → --></mml:mo> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mover> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi mathvariant=\"double-struck\">Z</mml:mi> </mml:mrow> <mml:mo>^<!-- ^ --></mml","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniqueness and stability for the solution of a nonlinear least squares problem","authors":"Meng Huang, Zhiqiang Xu","doi":"10.1090/mcom/3918","DOIUrl":"https://doi.org/10.1090/mcom/3918","url":null,"abstract":"In this paper, we focus on the nonlinear least squares: $mbox{min}_{mathbf{x} in mathbb{H}^d}| |Amathbf{x}|-mathbf{b}|$ where $Ain mathbb{H}^{mtimes d}$, $mathbf{b} in mathbb{R}^m$ with $mathbb{H} in {mathbb{R},mathbb{C} }$ and consider the uniqueness and stability of solutions. Such problem arises, for instance, in phase retrieval and absolute value rectification neural networks. For the case where $mathbf{b}=|Amathbf{x}_0|$ for some $mathbf{x}_0in mathbb{H}^d$, many results have been developed to characterize the uniqueness and stability of solutions. However, for the case where $mathbf{b} neq |Amathbf{x}_0| $ for any $mathbf{x}_0in mathbb{H}^d$, there is no existing result for it to the best of our knowledge. In this paper, we first focus on the uniqueness of solutions and show for any matrix $Ain mathbb{H}^{m times d}$ there always exists a vector $mathbf{b} in mathbb{R}^m$ such that the solution is not unique. But, in real case, such ``bad'' vectors $mathbf{b}$ are negligible, namely, if $mathbf{b} in mathbb{R}_{+}^m$ does not lie in some measure zero set, then the solution is unique. We also present some conditions under which the solution is unique. For the stability of solutions, we prove that the solution is never uniformly stable. But if we restrict the vectors $mathbf{b}$ to any convex set then it is stable.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tamed stability of finite difference schemes for the transport equation on the half-line","authors":"Lucas Coeuret","doi":"10.1090/mcom/3901","DOIUrl":"https://doi.org/10.1090/mcom/3901","url":null,"abstract":"In this paper, we prove that, under precise spectral assumptions, some finite difference approximations of scalar leftgoing transport equations on the positive half-line with numerical boundary conditions are <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script l Superscript 1\"> <mml:semantics> <mml:msup> <mml:mi>ℓ<!-- ℓ --></mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">ell ^1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-stable but <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script l Superscript q\"> <mml:semantics> <mml:msup> <mml:mi>ℓ<!-- ℓ --></mml:mi> <mml:mi>q</mml:mi> </mml:msup> <mml:annotation encoding=\"application/x-tex\">ell ^q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-unstable for any <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q greater-than 1\"> <mml:semantics> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">q&gt;1</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The proof relies on the accurate description of the Green’s function for a particular family of finite rank perturbations of Toeplitz operators whose essential spectrum belongs to the closed unit disk and with a simple eigenvalue of modulus <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1\"> <mml:semantics> <mml:mn>1</mml:mn> <mml:annotation encoding=\"application/x-tex\">1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> embedded into the essential spectrum.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Error estimates of the time-splitting methods for the nonlinear Schrödinger equation with semi-smooth nonlinearity","authors":"Weizhu Bao, Chushan Wang","doi":"10.1090/mcom/3900","DOIUrl":"https://doi.org/10.1090/mcom/3900","url":null,"abstract":"We establish error bounds of the Lie-Trotter time-splitting sine pseudospectral method for the nonlinear Schrödinger equation (NLSE) with semi-smooth nonlinearity <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f left-parenthesis rho right-parenthesis equals rho Superscript sigma\"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>ρ<!-- ρ --></mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>ρ<!-- ρ --></mml:mi> <mml:mi>σ<!-- σ --></mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">f(rho ) = rho ^sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"rho equals StartAbsoluteValue psi EndAbsoluteValue squared\"> <mml:semantics> <mml:mrow> <mml:mi>ρ<!-- ρ --></mml:mi> <mml:mo>=</mml:mo> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:msup> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mo stretchy=\"false\">|</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">rho =|psi |^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the density with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"psi\"> <mml:semantics> <mml:mi>ψ<!-- ψ --></mml:mi> <mml:annotation encoding=\"application/x-tex\">psi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> the wave function and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"sigma greater-than 0\"> <mml:semantics> <mml:mrow> <mml:mi>σ<!-- σ --></mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">sigma &gt;0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the exponent of the semi-smooth nonlinearity. Under the assumption of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H squared\"> <mml:semantics> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">H^2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-solution of the NLSE, we prove error bounds at <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O left-parenthesis tau Superscript one half plus sigma Baseline plus h Superscript 1 plus 2 sigma Baseline right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msup> <mml:mi>τ<!-- τ --></mml:mi> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>+</mml:mo> <mml:mi>σ<!-- σ --></mml:mi> </mml:mrow> <","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135547406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computing quadratic points on modular curves 𝑋₀(𝑁)","authors":"Nikola Adžaga, Timo Keller, Philippe Michaud-Jacobs, Filip Najman, Ekin Ozman, Borna Vukorepa","doi":"10.1090/mcom/3902","DOIUrl":"https://doi.org/10.1090/mcom/3902","url":null,"abstract":"In this paper we improve on existing methods to compute quadratic points on modular curves and apply them to successfully find all the quadratic points on all modular curves <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X 0 left-parenthesis upper N right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">X_0(N)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of genus up to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"8\"> <mml:semantics> <mml:mn>8</mml:mn> <mml:annotation encoding=\"application/x-tex\">8</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and genus up to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"10\"> <mml:semantics> <mml:mn>10</mml:mn> <mml:annotation encoding=\"application/x-tex\">10</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding=\"application/x-tex\">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> prime, for which they were previously unknown. The values of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\"> <mml:semantics> <mml:mi>N</mml:mi> <mml:annotation encoding=\"application/x-tex\">N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> we consider are contained in the set <disp-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper L equals StartSet 58 comma 68 comma 74 comma 76 comma 80 comma 85 comma 97 comma 98 comma 100 comma 103 comma 107 comma 109 comma 113 comma 121 comma 127 EndSet period\"> <mml:semantics> <mml:mrow> <mml:mrow class=\"MJX-TeXAtom-ORD\"> <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">L</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo> <mml:mn>58</mml:mn> <mml:mo>,</mml:mo> <mml:mn>68</mml:mn> <mml:mo>,</mml:mo> <mml:mn>74</mml:mn> <mml:mo>,</mml:mo> <mml:mn>76</mml:mn> <mml:mo>,</mml:mo> <mml:mn>80</mml:mn> <mml:mo>,</mml:mo> <mml:mn>85</mml:mn> <mml:mo>,</mml:mo> <mml:mn>97</mml:mn> <mml:mo>,</mml:mo> <mml:mn>98</mml:mn> <mml:mo>,</mml:mo> <mml:mn>100</mml:mn> <mml:mo>,</mml:mo> <mml:mn>103</mml:mn> <mml:mo>,</mml:mo> <mml:mn>107</mml:mn> <mml:mo>,</mml:mo> <mml:mn>109</mml:mn> <mml:mo>,</mml:mo> <mml:mn>113</mml:mn> <mml:mo>,</mml:mo> <mml:mn>121</mml:mn> <mml:mo>,</mml:mo> <mml:mn>127</mml:mn> <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo> <mml:mo>.</mml:mo> </mml:mrow> <mml:ann","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135689172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Randomizing the trapezoidal rule gives the optimal RMSE rate in Gaussian Sobolev spaces","authors":"Takashi Goda, Yoshihito Kazashi, Yuya Suzuki","doi":"10.1090/mcom/3910","DOIUrl":"https://doi.org/10.1090/mcom/3910","url":null,"abstract":"","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135295313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimization of differential equations and algebraic values of 𝐸-functions","authors":"Alin Bostan, Tanguy Rivoal, Bruno Salvy","doi":"10.1090/mcom/3912","DOIUrl":"https://doi.org/10.1090/mcom/3912","url":null,"abstract":"","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135428054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical analysis for electromagnetic scattering from nonlinear boundary conditions","authors":"Jörg Nick","doi":"10.1090/mcom/3914","DOIUrl":"https://doi.org/10.1090/mcom/3914","url":null,"abstract":"","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135579674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hensel lifting algorithms for quadratic forms","authors":"Simon Brandhorst, Davide Veniani","doi":"10.1090/mcom/3909","DOIUrl":"https://doi.org/10.1090/mcom/3909","url":null,"abstract":"","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136072900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A kit for linear forms in three logarithms","authors":"Maurice Mignotte, Paul Voutier, Michel Laurent","doi":"10.1090/mcom/3908","DOIUrl":"https://doi.org/10.1090/mcom/3908","url":null,"abstract":"","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135096432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}