See Riemann hypothesis in All languages combined, or Wiktionary
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"etymology_text": "Named after German mathematician Bernhard Riemann (1826–1866), who first formulated and discussed the hypothesis.",
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{
"text": "The Riemann hypothesis has deep implications about the distribution of prime numbers.",
"type": "example"
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{
"text": "1995, John Corning Carey, On Beurling's Approach to the Reimann Hypothesis, University of California, Berkeley, page 43,\nBut in the absence of such assumptions, the task of finding functions h∈ℱ₂ for which ‖1+h‖₂ is small is equivalent to proving the Riemann hypothesis, as we will now demonstrate."
},
{
"text": "2003, Marcus du Sautoy, The Music of the Primes, 2004, HarperCollins Publishers (Harper Perennial), page 10,\nA solution of the Riemann Hypothesis will have huge implications for many other mathematical problems."
},
{
"text": "2010, Samuel J. Patterson, The Riemann Hypothesis – a short history, Gerrit Dijk, Masato Wakayama (editors), Casimir Force, Casimir Operators and the Riemann Hypothesis, Walter de Gruyter, page 30,\nThe one problem proposed in Riemann's paper which remained unproved, the only one Riemann put forward explicitly as a conjecture, was the Riemann Hypothesis."
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"text": "2021, Naji Arwashan, The Riemann Hypothesis and the Distribution of Prime Numbers, Nova Science Publishers, page x,\nThe Riemann Hypothesis is considered by many accounts the single most important and difficult question in math today."
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"glosses": [
"The conjecture that the zeros of the Riemann zeta function exist only at the negative even integers and certain complex numbers whose real part is ½."
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"(mathematics, mathematical analysis, number theory) The conjecture that the zeros of the Riemann zeta function exist only at the negative even integers and certain complex numbers whose real part is ½."
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"code": "de",
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"sense": "conjecture about the zeros of the Riemann zeta function",
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"word": "Riemannsche Vermutung"
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"sense": "conjecture about the zeros of the Riemann zeta function",
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"word": "Riemannsche Hypothese"
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"sense": "conjecture about the zeros of the Riemann zeta function",
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"word": "Riemann-Hypothese"
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"code": "it",
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"sense": "conjecture about the zeros of the Riemann zeta function",
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"word": "ipotesi di Riemann"
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{
"code": "it",
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"sense": "conjecture about the zeros of the Riemann zeta function",
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"word": "congettura di Riemann"
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"word": "Riemann hypothesis"
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{
"etymology_text": "Named after German mathematician Bernhard Riemann (1826–1866), who first formulated and discussed the hypothesis.",
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"text": "The Riemann hypothesis has deep implications about the distribution of prime numbers.",
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},
{
"text": "1995, John Corning Carey, On Beurling's Approach to the Reimann Hypothesis, University of California, Berkeley, page 43,\nBut in the absence of such assumptions, the task of finding functions h∈ℱ₂ for which ‖1+h‖₂ is small is equivalent to proving the Riemann hypothesis, as we will now demonstrate."
},
{
"text": "2003, Marcus du Sautoy, The Music of the Primes, 2004, HarperCollins Publishers (Harper Perennial), page 10,\nA solution of the Riemann Hypothesis will have huge implications for many other mathematical problems."
},
{
"text": "2010, Samuel J. Patterson, The Riemann Hypothesis – a short history, Gerrit Dijk, Masato Wakayama (editors), Casimir Force, Casimir Operators and the Riemann Hypothesis, Walter de Gruyter, page 30,\nThe one problem proposed in Riemann's paper which remained unproved, the only one Riemann put forward explicitly as a conjecture, was the Riemann Hypothesis."
},
{
"text": "2021, Naji Arwashan, The Riemann Hypothesis and the Distribution of Prime Numbers, Nova Science Publishers, page x,\nThe Riemann Hypothesis is considered by many accounts the single most important and difficult question in math today."
}
],
"glosses": [
"The conjecture that the zeros of the Riemann zeta function exist only at the negative even integers and certain complex numbers whose real part is ½."
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"(mathematics, mathematical analysis, number theory) The conjecture that the zeros of the Riemann zeta function exist only at the negative even integers and certain complex numbers whose real part is ½."
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{
"code": "de",
"lang": "German",
"sense": "conjecture about the zeros of the Riemann zeta function",
"tags": [
"feminine"
],
"word": "Riemannsche Vermutung"
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"sense": "conjecture about the zeros of the Riemann zeta function",
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{
"code": "de",
"lang": "German",
"sense": "conjecture about the zeros of the Riemann zeta function",
"tags": [
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"word": "Riemannsche Hypothese"
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{
"code": "de",
"lang": "German",
"sense": "conjecture about the zeros of the Riemann zeta function",
"tags": [
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],
"word": "Riemann-Hypothese"
},
{
"code": "it",
"lang": "Italian",
"sense": "conjecture about the zeros of the Riemann zeta function",
"tags": [
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"word": "ipotesi di Riemann"
},
{
"code": "it",
"lang": "Italian",
"sense": "conjecture about the zeros of the Riemann zeta function",
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"word": "Riemann hypothesis"
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