Solomon Friedberg

Publications, 2000 on

Press here to see full publication list.

(with B. Brubaker, D. Bump) Matrix coefficients and Iwahori-Hecke algebra modules, submitted. Preprint here. Also on the arxiv, here.

(with D. Ginzburg) Criteria for the existence of cuspidal theta representations, submitted. Preprint here. Also on the arxiv, here.

(with D. Ginzburg) On the genericity of Eisenstein series and their residues for covers of GLm, to appear inInternational Mathematics Research Notices (IMRN). Preprint here. Also on the arxiv, here.

(with D. Ginzburg) Theta functions on covers of symplectic groups, to appear inAutomorphic Forms, L-functions and Number Theory,a special issue ofBIMSin honor of Prof. Freydoon Shahidi's 70th birthday. Preprint (Version 2, February 17, 2016) here. Also on the arxiv (slightly older version), here.

(with D. Ginzburg) Descent and theta functions for metaplectic groups, to appear inJournal of the European Mathematical Society (JEMS). Please note that the on-line version of July 2015 is significantly revised from and supersedes the earlier version. Available here and (arxiv) here.

(with L. Zhang) Tokuyama-type formulas for type B, to appear in theIsrael Journal of Mathematics. Preprint here. Also on the arxiv, here.

(with B. Brubaker) Whittaker coefficients of metaplectic Eisenstein series,Geometric and Functional Analysis(GAFA)25(4) (2015), 1180-1239. Available on-line here. Preprint here. Supplementary calculations here. Also on the arxiv (slightly older version), here. DOI: 10.1007/s00039-015-0329-4.

(with L. Zhang), Eisenstein series on covers of odd orthogonal groups,American Journal of Mathematics137(2015), 953-1011. For a pdf, click here. Also on the arxiv, here. DOI: 10.1353/ajm.2015.003.

(with D. Ginzburg) Metaplectic theta functions and global integrals,Journal of Number Theory146(2015), 134-149 (special issue in memory of Steve Rallis). For a pdf, click here. Also on the arxiv, here. DOI:10.1016/j.jnt.2014.04.001.

(with B. Brubaker, D. Bump) Unique functionals and representations of Hecke algebras,Pacific Journal of Mathematics260(2) (2012), 381-394. (This is the issue in memory of Jonathan Rogawski.) For a .pdf, click here. DOI 10.2140/pjm.2012.260.381.

Multiple Dirichlet Series, L-Functions and Automorphic Forms, edited by D. Bump, S. Friedberg and D. Goldfeld, Progress in Mathematics, Vol. 300, Birkhäuser Boston, 2012.

(with B. Brubaker, D. Bump, G. Chinta and P. E. Gunnells) Metaplectic ice, in: Multiple Dirichlet Series, L-Functions and Automorphic Forms (Bump, Friedberg, and Goldfeld, eds.), Progress in Mathematics, Vol. 300, Birkhäuser Boston 2012, pp. 65-92. For a .pdf of the preprint, click here. Also on the arxiv, here. DOI: 10.1007/978-0-8176-8334-4.

(with G. Chinta, J. Hoffstein) Double Dirichlet series and theta functions, in: Contributions in Analytic and Algebraic Number Theory (Blomer, Mihăilescu, eds.), Springer Proceedings in Math., Vol. 9, Springer, 2012, pp.149-170. For a .pdf, click here.

(with B. Brubaker, D. Bump and J. Hoffstein), Coefficients of the n-fold theta function and Weyl group multiple Dirichlet series, in: Contributions in Analytic and Algebraic Number Theory (Blomer, Mihăilescu, eds.), Springer Proceedings in Math., Vol. 9, Springer, 2012, pp. 83-95. For a .pdf, click here.

Teaching teachers: roles for mathematicians (Preparando profesores: el papel de los matemáticos), Pensamiento Educativo, Revista de Investigación Educacional Latinoamericana

49(1) (2012), 32-39. For the article, click here.(with B. Brubaker, D. Bump) Eisenstein series, crystals and ice, Notices of the American Mathematical Society 58 (2011), 1563-1571. For a .pdf click here.

(with B. Brubaker, D. Bump), Schur polynomials and the Yang-Baxter equation, Communications in Mathematical Physics 308 (2011), 281-301. For a .pdf file, click here. Also on the arxiv, here.

(with B. Brubaker, D. Bump), Weyl group multiple Dirichlet series, Eisenstein series and crystal bases, Annals of Mathematics 173 (2011), 1081-1120. For a .pdf file, click here.

(with B. Brubaker, D. Bump), Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory, Annals of Mathematics Studies, Volume 175, Princeton University Press, 2011. For a .pdf file (137 pages) of an earlier version of the manuscript, click here. A good deal has been added since then.

Euler products and twisted Euler products, in: Automorphic forms and the Langlands Program (Ji, Liu, Yau and Zheng, eds.), Advanced Lectures in Mathematics, Vol. 9, International Press, 2010, pp. 176--198. Published jointly by International Press and by Higher Education Press of China. For a .pdf file, click here.

(with B. Brubaker, D. Bump) Gauss sum combinatorics and metaplectic Eisenstein series, in: Automorphic Forms and L-functions I: Global Aspects (Ginzburg, Lapid and Soudry, eds.), Contemporary Mathematics Vol. 488, American Mathematical Society, 2009, pp. 61--81. For a .pdf file, click here.

(with G. Chinta, P. E. Gunnells), On the p-parts of quadratic Weyl group multiple Dirichlet series,

Journal für die Reine und Angewandte Mathematik623 (2008), 1--23. For a .pdf file, click here. Also on the arxiv, here.

(with B. Brubaker, D. Bump) Twisted Weyl group multiple Dirichlet series: the stable case, in: Eisenstein Series and Applications (Gan, Kudla and Tschinkel, eds.), Progress in Math Vol. 258, Birkhäuser, 2008, pp. 1--26. For a .pdf file, click here.

(with B. Brubaker, D. Bump, J. Hoffstein) Weyl group multiple Dirichlet series III: Eisenstein series and twisted unstable A_r,

Annals of Mathematics166 (2007), 293--316. For a .pdf file, click here.

There are two web-only companion papers to the above paper (each joint work with Brubaker, Bump and Hoffstein). The first is: "Metaplectic Eisenstein series on GL(3)". This contains more details about some of the foundational material and proofs in "Weyl group multiple Dirichlet series III". For a .pdf file, click here. The second is: "Gelfand-Tsetlin interpretation of Chinta's A_5 polynomial". For a .pdf file, click here, but do not print it, as it is 1,012 pages!

(with A. Ash) Hecke L-functions and the distribution of totally positive integers, Canadian Journal of Mathematics 59 (2007), 673--695. For a .pdf file, click here.

Teaching mathematics graduate students to teach: an international perspective, in: Enhancing University Mathematics, Proceedings of the First KAIST International Symposium on Teaching (Ko and Arganbright, eds.), Issues in Mathematics Education Vol. 14, American Mathematical Society, Providence RI, 2007, pp. 51--55. For a .pdf file, click here.

A previous version of these proceedings was circulated as a bound volume Proceedings of the First KAIST International Symposium on Enhancing University Mathematics Teaching, Korean Advanced Institute of Science and Technology, Daejeon, Korea, 2005, and this article is on pages 177--181 of that volume. There are minor differences between the two versions.(with B. Brubaker, D. Bump) Weyl group multiple Dirichlet series II: the stable case,

Inventiones Math165(2006), 325--355. For a .pdf file, click here. For an older .pdf version of the paper that contains a more coordinatized treatment, click here.

(with D. Bump, D. Ginzburg) Lifting automorphic representations on the double covers of orthogonal groups, Duke Mathematical Journal

(with G. Chinta, J. Hoffstein) Multiple Dirichlet series and automorphic forms,131(2006), 363--396. For a .ps file, click here. For a .pdf file, click here.

Proc. Symp. Pure Math.75(2006), 3--41. For a .pdf file, click here.

(with B. Brubaker, D. Bump, G. Chinta, J. Hoffstein) Weyl group multiple Dirichlet series I,

Proc. Symp. Pure Math.75(2006), 91--114. For a .ps file, click here.

Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory, edited by S. Friedberg (Managing Editor), D. Bump, D. Goldfeld, J. Hoffstein,

Proceedings of Symposia in Pure Mathematics, Volume 75, American Mathematical Society (Providence, RI), 2006.

(with G. Chinta, J. Hoffstein) Asypmtotics for sums of twisted L-functions and applications, in: Automorphic Representations, L-functions and Applications: Progress and Prospects, Ohio State University Mathematical Research Institute Publications 11, de Gruyter, 2005, pp. 75--94. For a .pdf file, click here.

(with B. Brubaker, J. Hoffstein) Cubic twists of GL(2) automorphic L-functions, Inventiones Math. 160 (2005), 31--58. For a .pdf file, click here.

Teaching mathematics graduate students how to teach, Notices of the American Mathematical Society 52 (2005), 842--847. For a .pdf file, click here.

(with D. Bump, J. Hoffstein) Sums of twisted GL(3) automorphic L-functions, in

Contributions to Automorphic Forms, Geometry and Arithmetic(H. Hida, D. Ramakrishnan and F. Shahidi, eds.), Johns Hopkins Univ. Press, 2004, pp. 131--162. For a .pdf file, click here.

(with B. Fisher) Double Dirichlet series over function fields,

Compositio Mathematica 140(2004), 613--630. For a .pdf file, click here.(with J. Hoffstein, D. Lieman) Double Dirichlet series and the n-th order twists of Hecke L-series,

Mathematische Annalen327 (2003), 315--338.

(with D. Bump, D. Ginzburg) Small representations for odd orthogonal groups,

International Mathematical Research Notices2003:25(2003),1363--1393.(with B. Fisher) Sums of twisted GL(2) L-functions over function fields,

Duke Mathematical Journal117(2003), 543--570.A note on base change, identitites involving tau(n), and a congruence of Ramanujan,

Ramanujan Journal7, No. 1-3 (2003), 165--168 (Robert A. Rankin special memorial issues).

(with D. Bump, D. Ginzburg) On the cubic Shimura lift for PGL

_{3},Israel J. of Mathematics126(2001), 289--308.S. Friedberg and the BCCase Development Team,

Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom, Issues in Mathematics Education Volume 10, American Mathematical Society, Providence RI, 2001. Faculty Edition ISBN 0-8218-2875-4; Graduate Student Edition ISBN 0-8218-2823-1.(with D. Bump, D. Ginzburg) A Rankin-Selberg integral using the automorphic minimal representation of SO(7),

J. Ramanujan Math. Society15(2000), 81--124.

Department of Mathematics

Boston College

Chestnut Hill, MA 02467-3806

(617) 552-3002

Solomon.Friedberg@bc.eduMath Department Home Page