Relevant bibliographies by topics / Selberg class

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Selberg class'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 February 2022

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Journal articles on the topic "Selberg class"

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Dixit, Anup B., and V. Kumar Murty. "The Lindelöf class of L-functions II." International Journal of Number Theory 15, no. 10 (2019): 2201–21. http://dx.doi.org/10.1142/s1793042119501215.

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In 2002, the second author introduced a class of [Formula: see text]-functions [Formula: see text], which contains the Selberg class and forms a ring. In this paper, we study this class and prove that the invariant [Formula: see text], which is the generalization of degree in the Selberg class cannot take non-integer values between [Formula: see text] and [Formula: see text]. We also study the ring structure of [Formula: see text] showing that it is non-Noetherian.
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Kaczorowski, Jerzy, Giuseppe Molteni, Alberto Perelli, Jörn Steuding, and Jürgen Wolfart. "Hecke's theory and the Selberg class." Functiones et Approximatio Commentarii Mathematici 35 (January 2006): 183–93. http://dx.doi.org/10.7169/facm/1229442622.

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Kaczorowski, Jerzy, and Alberto Perelli. "Factorization in the extended Selberg class." Functiones et Approximatio Commentarii Mathematici 31 (2003): 109–17. http://dx.doi.org/10.7169/facm/1538186642.

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Laurinčikas, A., and R. Macaitienė. "Discrete Universality in the Selberg Class." Proceedings of the Steklov Institute of Mathematics 299, no. 1 (2017): 143–56. http://dx.doi.org/10.1134/s0081543817080107.

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5

Soundararajan, K. "Strong Multiplicity One for the Selberg Class." Canadian Mathematical Bulletin 47, no. 3 (2004): 468–74. http://dx.doi.org/10.4153/cmb-2004-046-0.

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Kaczorowski, Jerzy, and Alberto Perelli. "Strong multiplicity one for the Selberg class." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 332, no. 11 (2001): 963–68. http://dx.doi.org/10.1016/s0764-4442(01)01984-x.

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Soundararajan, K. "Degree 1 elements of the Selberg class." Expositiones Mathematicae 23, no. 1 (2005): 65–70. http://dx.doi.org/10.1016/j.exmath.2005.01.013.

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Farmer, Michael. "Strong multiplicity one for the Selberg class." Mathematika 67, no. 3 (2021): 627–38. http://dx.doi.org/10.1112/mtk.12093.

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Kaczorowski, Jerzy, and Alberto Perelli. "On the Rankin–Selberg convolution of degree 2 functions from the extended Selberg class." Banach Center Publications 118 (2019): 25–35. http://dx.doi.org/10.4064/bc118-2.

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10

Omar, Sami, and Raouf Ouni. "A note on Li’s coefficients for Hecke L-functions." International Journal of Number Theory 13, no. 07 (2017): 1747–53. http://dx.doi.org/10.1142/s1793042117501007.

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Recently, the Li criterion for the Riemann hypothesis has been extended for a general class of [Formula: see text]-functions, so-called the Selberg class [S. Omar and K. Mazhouda, Le critère de Li et l’hypothèse de Riemann pour la classe de Selberg, J. Number Theory 125(1) (2007) 50–58; Corrigendum et addendum à “Le critère de Li et l’hypothèse de Riemann pour la classe de Selberg” [J. Number Theory 125(1) (2007) 50–58], J. Number Theory 130(4) (2010) 1109–1114]. Further numerical computations have been done to verify the positivity of some Li coefficients for the Dirichlet [Formula: see text]
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Dissertations / Theses on the topic "Selberg class"

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Rehberg, Martin [Verfasser], Jörn [Gutachter] Steuding, and Kai [Gutachter] Bruchlos. "Weighted uniform distribution related to primes and the Selberg Class / Martin Rehberg ; Gutachter: Jörn Steuding, Kai Bruchlos." Würzburg : Universität Würzburg, 2020. http://d-nb.info/1215500890/34.

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2

Bauer-Price, Pia. "The Selberg Trace Formula for PSL(2, OK) for imaginary quadratic number fields K of arbitrary class number." Bonn : [s.n.], 1991. http://catalog.hathitrust.org/api/volumes/oclc/26531368.html.

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Šimėnas, Raivydas. "Riemann'o hipotezės Speiser'io ekvivalentas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2012~D_20140704_171541-67476.

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A. Speiser'is parodė, kad Riemann'o hipotezė yra ekvivalenti tam, kad Riemann'o dzeta funkcijos išvestinė neturi netrivialių nulių į kairę nuo kritinės tiesės. Kiekybinis šio fakto rezultatas buvo pasiektas N. Levinsono ir H. Montgomerio. Šie rezultatai buvo apibendrinti daugeliui dzeta funkcijų, kurioms tikimasi, kad Riemann'o hipotezė galioja. Šiame darbe mes apibendriname Speiser'io ekvivalentą dzeta-funkcijoms. Mes tiriame sąryšį tarp netrivialių nulių išplėstinės Selbergo klasės funkcijoms ir jų išvestinėms šiame regione. Šiai klasei priklauso ir funkcijos, kurioms Riemann'o hipotezė nete
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Roton, Anne-Gwénaëlle de. "Généralisation du critère de Beurling-Nyman à la classe de Selberg." Bordeaux 1, 2003. http://www.theses.fr/2003BOR12768.

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Rehberg, Martin. "Weighted uniform distribution related to primes and the Selberg Class." Doctoral thesis, 2020. https://doi.org/10.25972/OPUS-20925.

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In the thesis at hand, several sequences of number theoretic interest will be studied in the context of uniform distribution modulo one. In the first part we deduce for positive and real \(z\not=1\) a discrepancy estimate for the sequence \( \left((2\pi )^{-1}(\log z)\gamma_a\right) \), where \(\gamma_a\) runs through the positive imaginary parts of the nontrivial \(a\)-points of the Riemann zeta-function. If the considered imaginary parts are bounded by \(T\), the discrepancy of the sequence \( \left((2\pi )^{-1}(\log z)\gamma_a\right) \) tends to zero like \( (\log\log\log T)^{-1} \) as \(
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6

Droll, ANDREW. "Variations of Li's criterion for an extension of the Selberg class." Thesis, 2012. http://hdl.handle.net/1974/7352.

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In 1997, Xian-Jin Li gave an equivalence to the classical Riemann hypothesis, now referred to as Li's criterion, in terms of the non-negativity of a particular infinite sequence of real numbers. We formulate the analogue of Li's criterion as an equivalence for the generalized quasi-Riemann hypothesis for functions in an extension of the Selberg class, and give arithmetic formulae for the corresponding Li coefficients in terms of parameters of the function in question. Moreover, we give explicit non-negative bounds for certain sums of special values of polygamma functions, involved in the arith
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Lamzouri, Youness. "Sur la distribution des valeurs de la fonction zêta de Riemann et des fonctions L au bord de la bande critque." Thèse, 2009. http://hdl.handle.net/1866/6626.

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Books on the topic "Selberg class"

1

D, Goldfeld, ed. Collected works of Hervé Jacquet. American Mathematical Society, 2011.

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Book chapters on the topic "Selberg class"

1

Murty, M. Ram. "The Selberg Class." In Problems in Analytic Number Theory. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3441-6_18.

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Murty, M. Ram. "The Selberg Class." In Problems in Analytic Number Theory. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3441-6_8.

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"The Selberg class: a survey." In Number Theory in Progress. De Gruyter, 1999. http://dx.doi.org/10.1515/9783110285581.953.

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"Random walk on knot diagrams, colored Jones polynomial and Ihara-Selberg zeta function." In Knots, Braids, and Mapping Class Groups—Papers Dedicated to Joan S. Birman. American Mathematical Society, 2001. http://dx.doi.org/10.1090/amsip/024/09.

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"Social Class and the Structuring of the Life Course in Norway and West Germany: David L. Featherman, L. Kevin Selbee, and Karl Ulrich Mayer." In Age Structuring in Comparative Perspective. Psychology Press, 2013. http://dx.doi.org/10.4324/9780203771402-12.

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